id sid tid token lemma pos american_scientific_journal-4118 1 1 58 58 NUM american_scientific_journal-4118 1 2 american american ADJ american_scientific_journal-4118 1 3 scientific scientific ADJ american_scientific_journal-4118 1 4 research research NOUN american_scientific_journal-4118 1 5 journal journal NOUN american_scientific_journal-4118 1 6 for for ADP american_scientific_journal-4118 1 7 engineering engineering NOUN american_scientific_journal-4118 1 8 , , PUNCT american_scientific_journal-4118 1 9 technology technology NOUN american_scientific_journal-4118 1 10 , , PUNCT american_scientific_journal-4118 1 11 and and CCONJ american_scientific_journal-4118 1 12 sciences science NOUN american_scientific_journal-4118 1 13 ( ( PUNCT american_scientific_journal-4118 1 14 asrjets asrjet NOUN american_scientific_journal-4118 1 15 ) ) PUNCT american_scientific_journal-4118 1 16 issn issn PROPN american_scientific_journal-4118 1 17 ( ( PUNCT american_scientific_journal-4118 1 18 print print NOUN american_scientific_journal-4118 1 19 ) ) PUNCT american_scientific_journal-4118 1 20 2313 2313 NUM american_scientific_journal-4118 1 21 - - SYM american_scientific_journal-4118 1 22 4410 4410 NUM american_scientific_journal-4118 1 23 , , PUNCT american_scientific_journal-4118 1 24 issn issn PROPN american_scientific_journal-4118 1 25 ( ( PUNCT american_scientific_journal-4118 1 26 online online ADJ american_scientific_journal-4118 1 27 ) ) PUNCT american_scientific_journal-4118 1 28 2313 2313 NUM american_scientific_journal-4118 1 29 - - SYM american_scientific_journal-4118 1 30 4402 4402 NUM american_scientific_journal-4118 1 31 Β© Β© PROPN american_scientific_journal-4118 1 32 global global ADJ american_scientific_journal-4118 1 33 society society NOUN american_scientific_journal-4118 1 34 of of ADP american_scientific_journal-4118 1 35 scientific scientific ADJ american_scientific_journal-4118 1 36 research research NOUN american_scientific_journal-4118 1 37 and and CCONJ american_scientific_journal-4118 1 38 researchers researcher NOUN american_scientific_journal-4118 1 39 http://asrjetsjournal.org/ http://asrjetsjournal.org/ VERB american_scientific_journal-4118 1 40 a a DET american_scientific_journal-4118 1 41 new new ADJ american_scientific_journal-4118 1 42 approach approach NOUN american_scientific_journal-4118 1 43 of of ADP american_scientific_journal-4118 1 44 bernoulli bernoulli PROPN american_scientific_journal-4118 1 45 sub sub ADJ american_scientific_journal-4118 1 46 - - ADJ american_scientific_journal-4118 1 47 ode ode ADJ american_scientific_journal-4118 1 48 method method NOUN american_scientific_journal-4118 1 49 to to PART american_scientific_journal-4118 1 50 solve solve VERB american_scientific_journal-4118 1 51 nonlinear nonlinear ADJ american_scientific_journal-4118 1 52 pdes pde NOUN american_scientific_journal-4118 1 53 md md PROPN american_scientific_journal-4118 1 54 . . PROPN american_scientific_journal-4118 1 55 abdus abdus PROPN american_scientific_journal-4118 1 56 salama salama PROPN american_scientific_journal-4118 1 57 * * PROPN american_scientific_journal-4118 1 58 , , PUNCT american_scientific_journal-4118 1 59 md md PROPN american_scientific_journal-4118 1 60 . . PROPN american_scientific_journal-4118 1 61 shafiqul shafiqul PROPN american_scientific_journal-4118 1 62 islamb islamb PROPN american_scientific_journal-4118 1 63 , , PUNCT american_scientific_journal-4118 1 64 md md PROPN american_scientific_journal-4118 1 65 . . PROPN american_scientific_journal-4118 1 66 hamidul hamidul PROPN american_scientific_journal-4118 1 67 islamc islamc PROPN american_scientific_journal-4118 1 68 , , PUNCT american_scientific_journal-4118 1 69 md md PROPN american_scientific_journal-4118 1 70 . . PUNCT american_scientific_journal-4118 2 1 abdul abdul PROPN american_scientific_journal-4118 2 2 azizd azizd PROPN american_scientific_journal-4118 2 3 a a PRON american_scientific_journal-4118 2 4 , , PUNCT american_scientific_journal-4118 2 5 bdept bdept NOUN american_scientific_journal-4118 2 6 . . PUNCT american_scientific_journal-4118 2 7 of of ADP american_scientific_journal-4118 2 8 mathematics mathematic NOUN american_scientific_journal-4118 2 9 , , PUNCT american_scientific_journal-4118 2 10 mawlana mawlana NOUN american_scientific_journal-4118 2 11 bhashani bhashani VERB american_scientific_journal-4118 2 12 science science NOUN american_scientific_journal-4118 2 13 and and CCONJ american_scientific_journal-4118 2 14 technology technology NOUN american_scientific_journal-4118 2 15 university university NOUN american_scientific_journal-4118 2 16 , , PUNCT american_scientific_journal-4118 2 17 tangail-1902 tangail-1902 NOUN american_scientific_journal-4118 2 18 , , PUNCT american_scientific_journal-4118 2 19 bangladesh bangladesh NOUN american_scientific_journal-4118 2 20 cdept cdept NOUN american_scientific_journal-4118 2 21 . . PUNCT american_scientific_journal-4118 3 1 of of ADP american_scientific_journal-4118 3 2 mathematics mathematic NOUN american_scientific_journal-4118 3 3 and and CCONJ american_scientific_journal-4118 3 4 physics physics NOUN american_scientific_journal-4118 3 5 , , PUNCT american_scientific_journal-4118 3 6 north north PROPN american_scientific_journal-4118 3 7 south south PROPN american_scientific_journal-4118 3 8 university university PROPN american_scientific_journal-4118 3 9 , , PUNCT american_scientific_journal-4118 3 10 dhaka dhaka PROPN american_scientific_journal-4118 3 11 , , PUNCT american_scientific_journal-4118 3 12 bangladesh bangladesh NOUN american_scientific_journal-4118 3 13 ddept ddept NOUN american_scientific_journal-4118 3 14 . . PUNCT american_scientific_journal-4118 4 1 of of ADP american_scientific_journal-4118 4 2 electronics electronic NOUN american_scientific_journal-4118 4 3 and and CCONJ american_scientific_journal-4118 4 4 telecommunication telecommunication NOUN american_scientific_journal-4118 4 5 engineering engineering NOUN american_scientific_journal-4118 4 6 , , PUNCT american_scientific_journal-4118 4 7 prime prime ADJ american_scientific_journal-4118 4 8 university university NOUN american_scientific_journal-4118 4 9 , , PUNCT american_scientific_journal-4118 4 10 dhaka-1216 dhaka-1216 NOUN american_scientific_journal-4118 4 11 , , PUNCT american_scientific_journal-4118 4 12 bangladesh bangladesh NOUN american_scientific_journal-4118 4 13 aemail aemail NOUN american_scientific_journal-4118 4 14 : : PUNCT american_scientific_journal-4118 4 15 salam.a.math03@gmail.com salam.a.math03@gmail.com X american_scientific_journal-4118 4 16 , , PUNCT american_scientific_journal-4118 4 17 bemail bemail NOUN american_scientific_journal-4118 4 18 : : PUNCT american_scientific_journal-4118 4 19 shafiquemath31@gmail.com shafiquemath31@gmail.com X american_scientific_journal-4118 4 20 cemail cemail NOUN american_scientific_journal-4118 4 21 : : PUNCT american_scientific_journal-4118 4 22 hamidul.islam@northsouth.edu hamidul.islam@northsouth.edu NOUN american_scientific_journal-4118 4 23 , , PUNCT american_scientific_journal-4118 4 24 demail demail NOUN american_scientific_journal-4118 4 25 : : PUNCT american_scientific_journal-4118 4 26 maaziz17@gmail.com maaziz17@gmail.com PROPN american_scientific_journal-4118 4 27 abstract abstract NOUN american_scientific_journal-4118 4 28 in in ADP american_scientific_journal-4118 4 29 this this DET american_scientific_journal-4118 4 30 paper paper NOUN american_scientific_journal-4118 4 31 , , PUNCT american_scientific_journal-4118 4 32 a a DET american_scientific_journal-4118 4 33 new new ADJ american_scientific_journal-4118 4 34 approach approach NOUN american_scientific_journal-4118 4 35 of of ADP american_scientific_journal-4118 4 36 the the DET american_scientific_journal-4118 4 37 bernoulli bernoulli PROPN american_scientific_journal-4118 4 38 sub sub ADJ american_scientific_journal-4118 4 39 - - ADJ american_scientific_journal-4118 4 40 ode ode ADJ american_scientific_journal-4118 4 41 method method NOUN american_scientific_journal-4118 4 42 is be AUX american_scientific_journal-4118 4 43 proposed propose VERB american_scientific_journal-4118 4 44 and and CCONJ american_scientific_journal-4118 4 45 this this DET american_scientific_journal-4118 4 46 method method NOUN american_scientific_journal-4118 4 47 is be AUX american_scientific_journal-4118 4 48 applied apply VERB american_scientific_journal-4118 4 49 to to PART american_scientific_journal-4118 4 50 solve solve VERB american_scientific_journal-4118 4 51 the the DET american_scientific_journal-4118 4 52 modified modify VERB american_scientific_journal-4118 4 53 liouville liouville NOUN american_scientific_journal-4118 4 54 equation equation NOUN american_scientific_journal-4118 4 55 and and CCONJ american_scientific_journal-4118 4 56 the the DET american_scientific_journal-4118 4 57 regularized regularize VERB american_scientific_journal-4118 4 58 long long ADJ american_scientific_journal-4118 4 59 wave wave NOUN american_scientific_journal-4118 4 60 equation equation NOUN american_scientific_journal-4118 4 61 . . PUNCT american_scientific_journal-4118 5 1 as as ADP american_scientific_journal-4118 5 2 a a DET american_scientific_journal-4118 5 3 result result NOUN american_scientific_journal-4118 5 4 some some DET american_scientific_journal-4118 5 5 new new ADJ american_scientific_journal-4118 5 6 traveling travel VERB american_scientific_journal-4118 5 7 wave wave NOUN american_scientific_journal-4118 5 8 solutions solution NOUN american_scientific_journal-4118 5 9 for for ADP american_scientific_journal-4118 5 10 them they PRON american_scientific_journal-4118 5 11 are be AUX american_scientific_journal-4118 5 12 successfully successfully ADV american_scientific_journal-4118 5 13 established establish VERB american_scientific_journal-4118 5 14 . . PUNCT american_scientific_journal-4118 6 1 when when SCONJ american_scientific_journal-4118 6 2 the the DET american_scientific_journal-4118 6 3 parameters parameter NOUN american_scientific_journal-4118 6 4 are be AUX american_scientific_journal-4118 6 5 taken take VERB american_scientific_journal-4118 6 6 as as ADP american_scientific_journal-4118 6 7 special special ADJ american_scientific_journal-4118 6 8 values value NOUN american_scientific_journal-4118 6 9 , , PUNCT american_scientific_journal-4118 6 10 the the DET american_scientific_journal-4118 6 11 solitary solitary ADJ american_scientific_journal-4118 6 12 wave wave NOUN american_scientific_journal-4118 6 13 solutions solution NOUN american_scientific_journal-4118 6 14 are be AUX american_scientific_journal-4118 6 15 originated originate VERB american_scientific_journal-4118 6 16 from from ADP american_scientific_journal-4118 6 17 these these DET american_scientific_journal-4118 6 18 traveling travel VERB american_scientific_journal-4118 6 19 wave wave NOUN american_scientific_journal-4118 6 20 solutions solution NOUN american_scientific_journal-4118 6 21 . . PUNCT american_scientific_journal-4118 7 1 further far ADV american_scientific_journal-4118 7 2 , , PUNCT american_scientific_journal-4118 7 3 graphical graphical ADJ american_scientific_journal-4118 7 4 representation representation NOUN american_scientific_journal-4118 7 5 of of ADP american_scientific_journal-4118 7 6 some some DET american_scientific_journal-4118 7 7 solutions solution NOUN american_scientific_journal-4118 7 8 are be AUX american_scientific_journal-4118 7 9 given give VERB american_scientific_journal-4118 7 10 to to PART american_scientific_journal-4118 7 11 visualize visualize VERB american_scientific_journal-4118 7 12 the the DET american_scientific_journal-4118 7 13 dynamics dynamic NOUN american_scientific_journal-4118 7 14 of of ADP american_scientific_journal-4118 7 15 the the DET american_scientific_journal-4118 7 16 equation equation NOUN american_scientific_journal-4118 7 17 . . PUNCT american_scientific_journal-4118 8 1 the the DET american_scientific_journal-4118 8 2 results result NOUN american_scientific_journal-4118 8 3 reveal reveal VERB american_scientific_journal-4118 8 4 that that SCONJ american_scientific_journal-4118 8 5 this this DET american_scientific_journal-4118 8 6 method method NOUN american_scientific_journal-4118 8 7 may may AUX american_scientific_journal-4118 8 8 be be AUX american_scientific_journal-4118 8 9 useful useful ADJ american_scientific_journal-4118 8 10 for for ADP american_scientific_journal-4118 8 11 solving solve VERB american_scientific_journal-4118 8 12 higher high ADJ american_scientific_journal-4118 8 13 order order NOUN american_scientific_journal-4118 8 14 nonlinear nonlinear ADJ american_scientific_journal-4118 8 15 partial partial ADJ american_scientific_journal-4118 8 16 differential differential NOUN american_scientific_journal-4118 8 17 equations equation NOUN american_scientific_journal-4118 8 18 . . PUNCT american_scientific_journal-4118 9 1 keywords keyword NOUN american_scientific_journal-4118 9 2 : : PUNCT american_scientific_journal-4118 9 3 modified modify VERB american_scientific_journal-4118 9 4 liouville liouville NOUN american_scientific_journal-4118 9 5 equation equation NOUN american_scientific_journal-4118 9 6 ; ; PUNCT american_scientific_journal-4118 9 7 regularized regularize VERB american_scientific_journal-4118 9 8 long long ADJ american_scientific_journal-4118 9 9 wave wave NOUN american_scientific_journal-4118 9 10 equation equation NOUN american_scientific_journal-4118 9 11 ; ; PUNCT american_scientific_journal-4118 9 12 traveling travel VERB american_scientific_journal-4118 9 13 wave wave NOUN american_scientific_journal-4118 9 14 solutions solution NOUN american_scientific_journal-4118 9 15 . . PUNCT american_scientific_journal-4118 10 1 1 1 X american_scientific_journal-4118 10 2 . . X american_scientific_journal-4118 10 3 introduction introduction NOUN american_scientific_journal-4118 10 4 the the DET american_scientific_journal-4118 10 5 investigation investigation NOUN american_scientific_journal-4118 10 6 of of ADP american_scientific_journal-4118 10 7 traveling travel VERB american_scientific_journal-4118 10 8 wave wave NOUN american_scientific_journal-4118 10 9 solutions(exact solutions(exact PROPN american_scientific_journal-4118 10 10 solutions solution NOUN american_scientific_journal-4118 10 11 ) ) PUNCT american_scientific_journal-4118 10 12 of of ADP american_scientific_journal-4118 10 13 nonlinear nonlinear ADJ american_scientific_journal-4118 10 14 partial partial ADJ american_scientific_journal-4118 10 15 differential differential NOUN american_scientific_journal-4118 10 16 equations(pdes equations(pde NOUN american_scientific_journal-4118 10 17 ) ) PUNCT american_scientific_journal-4118 10 18 plays play VERB american_scientific_journal-4118 10 19 an an DET american_scientific_journal-4118 10 20 important important ADJ american_scientific_journal-4118 10 21 role role NOUN american_scientific_journal-4118 10 22 not not PART american_scientific_journal-4118 10 23 only only ADV american_scientific_journal-4118 10 24 in in ADP american_scientific_journal-4118 10 25 theoretic theoretic ADJ american_scientific_journal-4118 10 26 research research NOUN american_scientific_journal-4118 10 27 but but CCONJ american_scientific_journal-4118 10 28 also also ADV american_scientific_journal-4118 10 29 in in ADP american_scientific_journal-4118 10 30 the the DET american_scientific_journal-4118 10 31 applications application NOUN american_scientific_journal-4118 10 32 . . PUNCT american_scientific_journal-4118 11 1 they they PRON american_scientific_journal-4118 11 2 describe describe VERB american_scientific_journal-4118 11 3 different different ADJ american_scientific_journal-4118 11 4 types type NOUN american_scientific_journal-4118 11 5 of of ADP american_scientific_journal-4118 11 6 physical physical ADJ american_scientific_journal-4118 11 7 systems system NOUN american_scientific_journal-4118 11 8 , , PUNCT american_scientific_journal-4118 11 9 ranging range VERB american_scientific_journal-4118 11 10 from from ADP american_scientific_journal-4118 11 11 gravitation gravitation NOUN american_scientific_journal-4118 11 12 to to ADP american_scientific_journal-4118 11 13 fluid fluid ADJ american_scientific_journal-4118 11 14 dynamics dynamic NOUN american_scientific_journal-4118 11 15 . . PUNCT american_scientific_journal-4118 12 1 the the DET american_scientific_journal-4118 12 2 interest interest NOUN american_scientific_journal-4118 12 3 of of ADP american_scientific_journal-4118 12 4 finding find VERB american_scientific_journal-4118 12 5 travelling travel VERB american_scientific_journal-4118 12 6 wave wave NOUN american_scientific_journal-4118 12 7 solutions solution NOUN american_scientific_journal-4118 12 8 of of ADP american_scientific_journal-4118 12 9 nonlinear nonlinear ADJ american_scientific_journal-4118 12 10 pdes pde NOUN american_scientific_journal-4118 12 11 is be AUX american_scientific_journal-4118 12 12 increasing increase VERB american_scientific_journal-4118 12 13 day day NOUN american_scientific_journal-4118 12 14 by by ADP american_scientific_journal-4118 12 15 day day NOUN american_scientific_journal-4118 12 16 and and CCONJ american_scientific_journal-4118 12 17 has have AUX american_scientific_journal-4118 12 18 now now ADV american_scientific_journal-4118 12 19 become become VERB american_scientific_journal-4118 12 20 a a DET american_scientific_journal-4118 12 21 hot hot ADJ american_scientific_journal-4118 12 22 topic topic NOUN american_scientific_journal-4118 12 23 to to ADP american_scientific_journal-4118 12 24 researchers researcher NOUN american_scientific_journal-4118 12 25 . . PUNCT american_scientific_journal-4118 13 1 in in ADP american_scientific_journal-4118 13 2 recent recent ADJ american_scientific_journal-4118 13 3 years year NOUN american_scientific_journal-4118 13 4 , , PUNCT american_scientific_journal-4118 13 5 many many ADJ american_scientific_journal-4118 13 6 researchers researcher NOUN american_scientific_journal-4118 13 7 who who PRON american_scientific_journal-4118 13 8 are be AUX american_scientific_journal-4118 13 9 interested interested ADJ american_scientific_journal-4118 13 10 in in ADP american_scientific_journal-4118 13 11 the the DET american_scientific_journal-4118 13 12 nonlinear nonlinear ADJ american_scientific_journal-4118 13 13 physical physical ADJ american_scientific_journal-4118 13 14 phenomena phenomenon NOUN american_scientific_journal-4118 13 15 have have AUX american_scientific_journal-4118 13 16 investigated investigate VERB american_scientific_journal-4118 13 17 exact exact ADJ american_scientific_journal-4118 13 18 solutions solution NOUN american_scientific_journal-4118 13 19 of of ADP american_scientific_journal-4118 13 20 nonlinear nonlinear ADJ american_scientific_journal-4118 13 21 pdes pde NOUN american_scientific_journal-4118 13 22 . . PUNCT american_scientific_journal-4118 14 1 ----------------------------------------------------------------------- ----------------------------------------------------------------------- PUNCT american_scientific_journal-4118 15 1 * * PUNCT american_scientific_journal-4118 15 2 corresponding correspond VERB american_scientific_journal-4118 15 3 author author NOUN american_scientific_journal-4118 15 4 . . PUNCT american_scientific_journal-4118 16 1 http://asrjetsjournal.org/ http://asrjetsjournal.org/ PROPN american_scientific_journal-4118 16 2 mailto:example@yahoo.com mailto:example@yahoo.com PROPN american_scientific_journal-4118 16 3 american american PROPN american_scientific_journal-4118 16 4 scientific scientific ADJ american_scientific_journal-4118 16 5 research research PROPN american_scientific_journal-4118 16 6 journal journal NOUN american_scientific_journal-4118 16 7 for for ADP american_scientific_journal-4118 16 8 engineering engineering NOUN american_scientific_journal-4118 16 9 , , PUNCT american_scientific_journal-4118 16 10 technology technology NOUN american_scientific_journal-4118 16 11 , , PUNCT american_scientific_journal-4118 16 12 and and CCONJ american_scientific_journal-4118 16 13 sciences science NOUN american_scientific_journal-4118 16 14 ( ( PUNCT american_scientific_journal-4118 16 15 asrjets asrjet NOUN american_scientific_journal-4118 16 16 ) ) PUNCT american_scientific_journal-4118 16 17 ( ( PUNCT american_scientific_journal-4118 16 18 2018 2018 NUM american_scientific_journal-4118 16 19 ) ) PUNCT american_scientific_journal-4118 16 20 volume volume NOUN american_scientific_journal-4118 16 21 44 44 NUM american_scientific_journal-4118 16 22 , , PUNCT american_scientific_journal-4118 16 23 no no DET american_scientific_journal-4118 16 24 1 1 NUM american_scientific_journal-4118 16 25 , , PUNCT american_scientific_journal-4118 16 26 pp pp ADV american_scientific_journal-4118 16 27 58 58 NUM american_scientific_journal-4118 16 28 - - SYM american_scientific_journal-4118 16 29 67 67 NUM american_scientific_journal-4118 16 30 59 59 NUM american_scientific_journal-4118 16 31 with with ADP american_scientific_journal-4118 16 32 the the DET american_scientific_journal-4118 16 33 development development NOUN american_scientific_journal-4118 16 34 of of ADP american_scientific_journal-4118 16 35 soliton soliton NOUN american_scientific_journal-4118 16 36 theory theory NOUN american_scientific_journal-4118 16 37 and and CCONJ american_scientific_journal-4118 16 38 the the DET american_scientific_journal-4118 16 39 application application NOUN american_scientific_journal-4118 16 40 of of ADP american_scientific_journal-4118 16 41 computer computer NOUN american_scientific_journal-4118 16 42 symbolic symbolic ADJ american_scientific_journal-4118 16 43 system system NOUN american_scientific_journal-4118 16 44 such such ADJ american_scientific_journal-4118 16 45 as as ADP american_scientific_journal-4118 16 46 maple maple NOUN american_scientific_journal-4118 16 47 and and CCONJ american_scientific_journal-4118 16 48 mathematica mathematica PROPN american_scientific_journal-4118 16 49 , , PUNCT american_scientific_journal-4118 16 50 many many ADJ american_scientific_journal-4118 16 51 powerful powerful ADJ american_scientific_journal-4118 16 52 methods method NOUN american_scientific_journal-4118 16 53 for for ADP american_scientific_journal-4118 16 54 obtaining obtain VERB american_scientific_journal-4118 16 55 exact exact ADJ american_scientific_journal-4118 16 56 solutions solution NOUN american_scientific_journal-4118 16 57 of of ADP american_scientific_journal-4118 16 58 nonlinear nonlinear ADJ american_scientific_journal-4118 16 59 evolution evolution NOUN american_scientific_journal-4118 16 60 equations equation NOUN american_scientific_journal-4118 16 61 are be AUX american_scientific_journal-4118 16 62 presented present VERB american_scientific_journal-4118 16 63 , , PUNCT american_scientific_journal-4118 16 64 such such ADJ american_scientific_journal-4118 16 65 as as ADP american_scientific_journal-4118 16 66 the the DET american_scientific_journal-4118 16 67 tanh tanh NOUN american_scientific_journal-4118 16 68 - - PUNCT american_scientific_journal-4118 16 69 method method NOUN american_scientific_journal-4118 16 70 [ [ X american_scientific_journal-4118 16 71 1 1 NUM american_scientific_journal-4118 16 72 - - SYM american_scientific_journal-4118 16 73 3 3 NUM american_scientific_journal-4118 16 74 ] ] PUNCT american_scientific_journal-4118 16 75 , , PUNCT american_scientific_journal-4118 16 76 the the DET american_scientific_journal-4118 16 77 extended extended ADJ american_scientific_journal-4118 16 78 tanh tanh NOUN american_scientific_journal-4118 16 79 method method NOUN american_scientific_journal-4118 16 80 [ [ X american_scientific_journal-4118 16 81 4 4 NUM american_scientific_journal-4118 16 82 - - SYM american_scientific_journal-4118 16 83 5 5 NUM american_scientific_journal-4118 16 84 ] ] PUNCT american_scientific_journal-4118 16 85 , , PUNCT american_scientific_journal-4118 16 86 the the DET american_scientific_journal-4118 16 87 jacobi jacobi PROPN american_scientific_journal-4118 16 88 elliptic elliptic ADJ american_scientific_journal-4118 16 89 function function NOUN american_scientific_journal-4118 16 90 expansion expansion NOUN american_scientific_journal-4118 16 91 [ [ X american_scientific_journal-4118 16 92 6 6 NUM american_scientific_journal-4118 16 93 - - SYM american_scientific_journal-4118 16 94 8 8 NUM american_scientific_journal-4118 16 95 ] ] PUNCT american_scientific_journal-4118 16 96 , , PUNCT american_scientific_journal-4118 16 97 the the DET american_scientific_journal-4118 16 98 bucland bucland NOUN american_scientific_journal-4118 16 99 transformation[9 transformation[9 NOUN american_scientific_journal-4118 16 100 - - SYM american_scientific_journal-4118 16 101 12 12 NUM american_scientific_journal-4118 16 102 ] ] PUNCT american_scientific_journal-4118 16 103 , , PUNCT american_scientific_journal-4118 16 104 the the DET american_scientific_journal-4118 16 105 homogeneous homogeneous ADJ american_scientific_journal-4118 16 106 balance balance NOUN american_scientific_journal-4118 16 107 method[13 method[13 PROPN american_scientific_journal-4118 16 108 ] ] PUNCT american_scientific_journal-4118 16 109 , , PUNCT american_scientific_journal-4118 16 110 the the DET american_scientific_journal-4118 16 111 inverse inverse NOUN american_scientific_journal-4118 16 112 scattering scattering NOUN american_scientific_journal-4118 16 113 method method NOUN american_scientific_journal-4118 16 114 [ [ X american_scientific_journal-4118 16 115 14 14 NUM american_scientific_journal-4118 16 116 ] ] PUNCT american_scientific_journal-4118 16 117 , , PUNCT american_scientific_journal-4118 16 118 the the DET american_scientific_journal-4118 16 119 variational variational ADJ american_scientific_journal-4118 16 120 iteration iteration NOUN american_scientific_journal-4118 16 121 method method NOUN american_scientific_journal-4118 16 122 [ [ X american_scientific_journal-4118 16 123 15 15 NUM american_scientific_journal-4118 16 124 ] ] PUNCT american_scientific_journal-4118 16 125 , , PUNCT american_scientific_journal-4118 16 126 the the DET american_scientific_journal-4118 16 127 exp exp NOUN american_scientific_journal-4118 16 128 - - PUNCT american_scientific_journal-4118 16 129 function function NOUN american_scientific_journal-4118 16 130 method method NOUN american_scientific_journal-4118 16 131 [ [ X american_scientific_journal-4118 16 132 16 16 NUM american_scientific_journal-4118 16 133 ] ] PUNCT american_scientific_journal-4118 16 134 , , PUNCT american_scientific_journal-4118 16 135 ( ( PUNCT american_scientific_journal-4118 16 136 g'/g)-expansion g'/g)-expansion NOUN american_scientific_journal-4118 16 137 method method NOUN american_scientific_journal-4118 16 138 [ [ X american_scientific_journal-4118 16 139 17 17 NUM american_scientific_journal-4118 16 140 ] ] PUNCT american_scientific_journal-4118 16 141 , , PUNCT american_scientific_journal-4118 16 142 modified modify VERB american_scientific_journal-4118 16 143 simple simple ADJ american_scientific_journal-4118 16 144 equation equation NOUN american_scientific_journal-4118 16 145 method method NOUN american_scientific_journal-4118 16 146 [ [ X american_scientific_journal-4118 16 147 18 18 NUM american_scientific_journal-4118 16 148 ] ] PUNCT american_scientific_journal-4118 16 149 , , PUNCT american_scientific_journal-4118 16 150 f f X american_scientific_journal-4118 16 151 - - PUNCT american_scientific_journal-4118 16 152 expansion expansion NOUN american_scientific_journal-4118 16 153 method[19 method[19 NOUN american_scientific_journal-4118 16 154 - - PUNCT american_scientific_journal-4118 16 155 20 20 NUM american_scientific_journal-4118 16 156 ] ] PUNCT american_scientific_journal-4118 16 157 and and CCONJ american_scientific_journal-4118 16 158 so so ADV american_scientific_journal-4118 16 159 on on ADV american_scientific_journal-4118 16 160 . . PUNCT american_scientific_journal-4118 17 1 in in ADP american_scientific_journal-4118 17 2 2011 2011 NUM american_scientific_journal-4118 17 3 , , PUNCT american_scientific_journal-4118 17 4 ben ben PROPN american_scientific_journal-4118 17 5 jing jing PROPN american_scientific_journal-4118 17 6 proposed propose VERB american_scientific_journal-4118 17 7 bernoulli bernoulli PROPN american_scientific_journal-4118 17 8 sub sub ADJ american_scientific_journal-4118 17 9 - - ADJ american_scientific_journal-4118 17 10 ode ode ADJ american_scientific_journal-4118 17 11 method method NOUN american_scientific_journal-4118 17 12 for for ADP american_scientific_journal-4118 17 13 finding find VERB american_scientific_journal-4118 17 14 exact exact ADJ american_scientific_journal-4118 17 15 solutions solution NOUN american_scientific_journal-4118 17 16 of of ADP american_scientific_journal-4118 17 17 nonlinear nonlinear ADJ american_scientific_journal-4118 17 18 pdes pde NOUN american_scientific_journal-4118 17 19 . . PUNCT american_scientific_journal-4118 18 1 after after ADP american_scientific_journal-4118 18 2 reducing reduce VERB american_scientific_journal-4118 18 3 the the DET american_scientific_journal-4118 18 4 nonliner nonliner NOUN american_scientific_journal-4118 18 5 pdes pde VERB american_scientific_journal-4118 18 6 𝑃𝑃(𝑒𝑒,𝑒𝑒𝑑𝑑 𝑃𝑃(𝑒𝑒,𝑒𝑒𝑑𝑑 PROPN american_scientific_journal-4118 18 7 , , PUNCT american_scientific_journal-4118 18 8 𝑒𝑒π‘₯π‘₯,𝑒𝑒𝑑𝑑𝑑𝑑 𝑒𝑒π‘₯π‘₯,𝑒𝑒𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-4118 18 9 , , PUNCT american_scientific_journal-4118 18 10 𝑒𝑒π‘₯π‘₯𝑑𝑑 𝑒𝑒π‘₯π‘₯𝑑𝑑 NOUN american_scientific_journal-4118 18 11 , , PUNCT american_scientific_journal-4118 18 12 𝑒𝑒π‘₯π‘₯π‘₯π‘₯ 𝑒𝑒π‘₯π‘₯π‘₯π‘₯ NOUN american_scientific_journal-4118 18 13 , , PUNCT american_scientific_journal-4118 18 14 … … PUNCT american_scientific_journal-4118 18 15 … … PUNCT american_scientific_journal-4118 18 16 ) ) PUNCT american_scientific_journal-4118 19 1 = = SYM american_scientific_journal-4118 19 2 0 0 NUM american_scientific_journal-4118 19 3 to to ADP american_scientific_journal-4118 19 4 nonlinear nonlinear ADJ american_scientific_journal-4118 19 5 odes ode NOUN american_scientific_journal-4118 19 6 0 0 NUM american_scientific_journal-4118 19 7 ) ) PUNCT american_scientific_journal-4118 19 8 , , PUNCT american_scientific_journal-4118 19 9 , , PUNCT american_scientific_journal-4118 19 10 , , PUNCT american_scientific_journal-4118 19 11 , , PUNCT american_scientific_journal-4118 19 12 , , PUNCT american_scientific_journal-4118 19 13 , , PUNCT american_scientific_journal-4118 19 14 ( ( PUNCT american_scientific_journal-4118 19 15 2 2 NUM american_scientific_journal-4118 19 16 = = NOUN american_scientific_journal-4118 19 17 β€²β€²β€²β€²βˆ’β€²β€²β€²β€²βˆ’ β€²β€²β€²β€²βˆ’β€²β€²β€²β€²βˆ’ NOUN american_scientific_journal-4118 19 18 llluucucuucup llluucucuucup NOUN american_scientific_journal-4118 19 19 by by ADP american_scientific_journal-4118 19 20 choosing choose VERB american_scientific_journal-4118 19 21 ) ) PUNCT american_scientific_journal-4118 19 22 , , PUNCT american_scientific_journal-4118 19 23 ( ( PUNCT american_scientific_journal-4118 19 24 ) ) PUNCT american_scientific_journal-4118 19 25 , , PUNCT american_scientific_journal-4118 19 26 ( ( PUNCT american_scientific_journal-4118 19 27 ΞΎutxu ΞΎutxu NOUN american_scientific_journal-4118 19 28 = = PUNCT american_scientific_journal-4118 19 29 where where SCONJ american_scientific_journal-4118 19 30 tcx tcx PROPN american_scientific_journal-4118 19 31 βˆ’=ΞΎ βˆ’=ΞΎ X american_scientific_journal-4118 19 32 , , PUNCT american_scientific_journal-4118 19 33 he he PRON american_scientific_journal-4118 19 34 assumed assume VERB american_scientific_journal-4118 19 35 the the DET american_scientific_journal-4118 19 36 solution solution NOUN american_scientific_journal-4118 19 37 of of ADP american_scientific_journal-4118 19 38 nonlinear nonlinear ADJ american_scientific_journal-4118 19 39 odes ode NOUN american_scientific_journal-4118 19 40 in in ADP american_scientific_journal-4118 19 41 the the DET american_scientific_journal-4118 19 42 form form NOUN american_scientific_journal-4118 19 43 𝑒𝑒 𝑒𝑒 ADP american_scientific_journal-4118 19 44 = = SYM american_scientific_journal-4118 19 45 βˆ‘ βˆ‘ PROPN american_scientific_journal-4118 19 46 π‘Žπ‘Žπ‘–π‘–π»π»π‘–π‘– π‘Žπ‘Žπ‘–π‘–π»π»π‘–π‘– PROPN american_scientific_journal-4118 19 47 , , PUNCT american_scientific_journal-4118 19 48 π‘šπ‘š π‘šπ‘š ADP american_scientific_journal-4118 19 49 𝑖𝑖=0 𝑖𝑖=0 PROPN american_scientific_journal-4118 19 50 where where SCONJ american_scientific_journal-4118 19 51 𝐻𝐻(πœ‰πœ‰ 𝐻𝐻(πœ‰πœ‰ NOUN american_scientific_journal-4118 19 52 ) ) PUNCT american_scientific_journal-4118 19 53 can can AUX american_scientific_journal-4118 19 54 be be AUX american_scientific_journal-4118 19 55 determined determine VERB american_scientific_journal-4118 19 56 from from ADP american_scientific_journal-4118 19 57 the the DET american_scientific_journal-4118 19 58 first first ADJ american_scientific_journal-4118 19 59 order order NOUN american_scientific_journal-4118 19 60 ode ode ADJ american_scientific_journal-4118 19 61 𝐻𝐻′ 𝐻𝐻′ NOUN american_scientific_journal-4118 19 62 = = PUNCT american_scientific_journal-4118 20 1 𝐻𝐻2 𝐻𝐻2 DET american_scientific_journal-4118 20 2 βˆ’ βˆ’ PUNCT american_scientific_journal-4118 20 3 𝐻𝐻 𝐻𝐻 PROPN american_scientific_journal-4118 20 4 [ [ PUNCT american_scientific_journal-4118 20 5 21 21 NUM american_scientific_journal-4118 20 6 - - SYM american_scientific_journal-4118 20 7 22 22 NUM american_scientific_journal-4118 20 8 ] ] PUNCT american_scientific_journal-4118 20 9 . . PUNCT american_scientific_journal-4118 21 1 but but CCONJ american_scientific_journal-4118 21 2 in in ADP american_scientific_journal-4118 21 3 our our PRON american_scientific_journal-4118 21 4 proposed propose VERB american_scientific_journal-4118 21 5 method method NOUN american_scientific_journal-4118 21 6 , , PUNCT american_scientific_journal-4118 21 7 we we PRON american_scientific_journal-4118 21 8 consider consider VERB american_scientific_journal-4118 21 9 a a DET american_scientific_journal-4118 21 10 set set NOUN american_scientific_journal-4118 21 11 of of ADP american_scientific_journal-4118 21 12 first first ADJ american_scientific_journal-4118 21 13 order order NOUN american_scientific_journal-4118 21 14 odes ode VERB american_scientific_journal-4118 21 15 in in ADP american_scientific_journal-4118 21 16 the the DET american_scientific_journal-4118 21 17 form form NOUN american_scientific_journal-4118 21 18 : : PUNCT american_scientific_journal-4118 21 19 0 0 NUM american_scientific_journal-4118 21 20 ) ) PUNCT american_scientific_journal-4118 21 21 ) ) PUNCT american_scientific_journal-4118 21 22 ( ( PUNCT american_scientific_journal-4118 21 23 ( ( PUNCT american_scientific_journal-4118 21 24 ) ) PUNCT american_scientific_journal-4118 21 25 ( ( PUNCT american_scientific_journal-4118 21 26 = = NOUN american_scientific_journal-4118 21 27 Β±β€² Β±β€² X american_scientific_journal-4118 21 28 nhh nhh NOUN american_scientific_journal-4118 21 29 ΞΎΞΎ ΞΎΞΎ ADP american_scientific_journal-4118 21 30 ( ( PUNCT american_scientific_journal-4118 21 31 where where SCONJ american_scientific_journal-4118 21 32 2β‰₯n 2β‰₯n NUM american_scientific_journal-4118 21 33 ) ) PUNCT american_scientific_journal-4118 21 34 instead instead ADV american_scientific_journal-4118 21 35 of of ADP american_scientific_journal-4118 21 36 𝐻𝐻′ 𝐻𝐻′ NOUN american_scientific_journal-4118 21 37 = = SYM american_scientific_journal-4118 21 38 ( ( PUNCT american_scientific_journal-4118 21 39 𝐻𝐻2 𝐻𝐻2 PRON american_scientific_journal-4118 21 40 βˆ’ βˆ’ NOUN american_scientific_journal-4118 21 41 𝐻𝐻 𝐻𝐻 PROPN american_scientific_journal-4118 21 42 ) ) PUNCT american_scientific_journal-4118 21 43 for for ADP american_scientific_journal-4118 21 44 getting get VERB american_scientific_journal-4118 21 45 a a DET american_scientific_journal-4118 21 46 set set NOUN american_scientific_journal-4118 21 47 of of ADP american_scientific_journal-4118 21 48 exact exact ADJ american_scientific_journal-4118 21 49 solutions solution NOUN american_scientific_journal-4118 21 50 and and CCONJ american_scientific_journal-4118 21 51 then then ADV american_scientific_journal-4118 21 52 a a DET american_scientific_journal-4118 21 53 set set NOUN american_scientific_journal-4118 21 54 of of ADP american_scientific_journal-4118 21 55 solitary solitary ADJ american_scientific_journal-4118 21 56 wave wave NOUN american_scientific_journal-4118 21 57 solutions solution NOUN american_scientific_journal-4118 21 58 in in ADP american_scientific_journal-4118 21 59 a a DET american_scientific_journal-4118 21 60 sequential sequential ADJ american_scientific_journal-4118 21 61 manner manner NOUN american_scientific_journal-4118 21 62 . . PUNCT american_scientific_journal-4118 22 1 here here ADV american_scientific_journal-4118 22 2 0 0 NUM american_scientific_journal-4118 22 3 ) ) PUNCT american_scientific_journal-4118 22 4 ) ) PUNCT american_scientific_journal-4118 22 5 ( ( PUNCT american_scientific_journal-4118 22 6 ( ( PUNCT american_scientific_journal-4118 22 7 ) ) PUNCT american_scientific_journal-4118 22 8 ( ( PUNCT american_scientific_journal-4118 22 9 = = NOUN american_scientific_journal-4118 22 10 Β±β€² Β±β€² X american_scientific_journal-4118 22 11 nhh nhh NOUN american_scientific_journal-4118 22 12 ΞΎΞΎ ΞΎΞΎ NOUN american_scientific_journal-4118 22 13 give give VERB american_scientific_journal-4118 22 14 the the DET american_scientific_journal-4118 22 15 following following NOUN american_scientific_journal-4118 22 16 ) ) PUNCT american_scientific_journal-4118 22 17 1.1 1.1 NUM american_scientific_journal-4118 22 18 ( ( PUNCT american_scientific_journal-4118 22 19 oddis,)1/(1])1 oddis,)1/(1])1 PROPN american_scientific_journal-4118 22 20 ( ( PUNCT american_scientific_journal-4118 22 21 [ [ PUNCT american_scientific_journal-4118 22 22 1,)1/(1])1 1,)1/(1])1 X american_scientific_journal-4118 22 23 ( ( PUNCT american_scientific_journal-4118 22 24 [ [ PUNCT american_scientific_journal-4118 22 25 1 1 NUM american_scientific_journal-4118 22 26 evenis,)1/(1])1 evenis,)1/(1])1 NOUN american_scientific_journal-4118 22 27 ( ( PUNCT american_scientific_journal-4118 22 28 [ [ PUNCT american_scientific_journal-4118 22 29 1 1 NUM american_scientific_journal-4118 22 30 ) ) PUNCT american_scientific_journal-4118 22 31 ( ( PUNCT american_scientific_journal-4118 22 32 11 11 NUM american_scientific_journal-4118 22 33 1 1 NUM american_scientific_journal-4118 22 34   PROPN american_scientific_journal-4118 22 35   PROPN american_scientific_journal-4118 22 36 ο£³ ο£³ ADJ american_scientific_journal-4118 22 37   PROPN american_scientific_journal-4118 22 38   PROPN american_scientific_journal-4118 22 39 ο£² ο£² ADP american_scientific_journal-4118 22 40 ο£± ο£± PROPN american_scientific_journal-4118 22 41 βˆ’βˆ’Β± βˆ’βˆ’Β± NOUN american_scientific_journal-4118 22 42 βˆ’ βˆ’ PUNCT american_scientific_journal-4118 23 1 βˆ’βˆ’Β± βˆ’βˆ’Β± ADV american_scientific_journal-4118 24 1 βˆ’βˆ’Β± βˆ’βˆ’Β± NOUN american_scientific_journal-4118 24 2 = = SYM american_scientific_journal-4118 24 3 nnncnnc nnncnnc PROPN american_scientific_journal-4118 25 1 nnnc nnnc INTJ american_scientific_journal-4118 25 2 h h NOUN american_scientific_journal-4118 25 3 ΞΎΞΎ ΞΎΞΎ ADP american_scientific_journal-4118 25 4 ΞΎ ΞΎ X american_scientific_journal-4118 25 5 ΞΎ ΞΎ X american_scientific_journal-4118 25 6 in in ADP american_scientific_journal-4118 25 7 this this DET american_scientific_journal-4118 25 8 method method NOUN american_scientific_journal-4118 25 9 , , PUNCT american_scientific_journal-4118 25 10 we we PRON american_scientific_journal-4118 25 11 will will AUX american_scientific_journal-4118 25 12 get get VERB american_scientific_journal-4118 25 13 the the DET american_scientific_journal-4118 25 14 solutions solution NOUN american_scientific_journal-4118 25 15 in in ADP american_scientific_journal-4118 25 16 terms term NOUN american_scientific_journal-4118 25 17 of of ADP american_scientific_journal-4118 25 18 ctx ctx NOUN american_scientific_journal-4118 25 19 nc nc PROPN american_scientific_journal-4118 25 20 βˆ’= βˆ’= PROPN american_scientific_journal-4118 25 21 βˆ’Β± βˆ’Β± X american_scientific_journal-4118 25 22 ΞΎ ΞΎ X american_scientific_journal-4118 25 23 ΞΎ ΞΎ PROPN american_scientific_journal-4118 25 24 , , PUNCT american_scientific_journal-4118 25 25 ] ] X american_scientific_journal-4118 25 26 ) ) PUNCT american_scientific_journal-4118 25 27 1 1 NUM american_scientific_journal-4118 25 28 ( ( PUNCT american_scientific_journal-4118 25 29 [ [ PUNCT american_scientific_journal-4118 25 30 1 1 NUM american_scientific_journal-4118 25 31 1 1 NUM american_scientific_journal-4118 25 32 , , PUNCT american_scientific_journal-4118 25 33 where where SCONJ american_scientific_journal-4118 25 34 the the DET american_scientific_journal-4118 25 35 singularities singularity NOUN american_scientific_journal-4118 25 36 occur occur VERB american_scientific_journal-4118 25 37 in in ADP american_scientific_journal-4118 25 38 the the DET american_scientific_journal-4118 25 39 case case NOUN american_scientific_journal-4118 25 40 of of ADP american_scientific_journal-4118 25 41 .0))(1(1 .0))(1(1 PUNCT american_scientific_journal-4118 26 1 = = SYM american_scientific_journal-4118 26 2 βˆ’βˆ’Β± βˆ’βˆ’Β± NOUN american_scientific_journal-4118 26 3 ctxnc ctxnc NOUN american_scientific_journal-4118 26 4 2 2 NUM american_scientific_journal-4118 26 5 . . PUNCT american_scientific_journal-4118 26 6 methodology methodology NOUN american_scientific_journal-4118 26 7 suppose suppose VERB american_scientific_journal-4118 26 8 that that SCONJ american_scientific_journal-4118 26 9 a a DET american_scientific_journal-4118 26 10 nonlinear nonlinear ADJ american_scientific_journal-4118 26 11 partial partial ADJ american_scientific_journal-4118 26 12 differential differential NOUN american_scientific_journal-4118 26 13 equation equation NOUN american_scientific_journal-4118 26 14 in in ADP american_scientific_journal-4118 26 15 two two NUM american_scientific_journal-4118 26 16 independent independent ADJ american_scientific_journal-4118 26 17 variables variable NOUN american_scientific_journal-4118 26 18 x x PUNCT american_scientific_journal-4118 26 19 and and CCONJ american_scientific_journal-4118 26 20 t t PROPN american_scientific_journal-4118 26 21 , , PUNCT american_scientific_journal-4118 26 22 is be AUX american_scientific_journal-4118 26 23 given give VERB american_scientific_journal-4118 26 24 by by ADP american_scientific_journal-4118 26 25 𝑃𝑃(𝑒𝑒,𝑒𝑒𝑑𝑑 𝑃𝑃(𝑒𝑒,𝑒𝑒𝑑𝑑 PROPN american_scientific_journal-4118 26 26 , , PUNCT american_scientific_journal-4118 26 27 𝑒𝑒π‘₯π‘₯,𝑒𝑒𝑑𝑑𝑑𝑑 𝑒𝑒π‘₯π‘₯,𝑒𝑒𝑑𝑑𝑑𝑑 NOUN american_scientific_journal-4118 26 28 , , PUNCT american_scientific_journal-4118 26 29 𝑒𝑒π‘₯π‘₯𝑑𝑑 𝑒𝑒π‘₯π‘₯𝑑𝑑 NOUN american_scientific_journal-4118 26 30 , , PUNCT american_scientific_journal-4118 26 31 𝑒𝑒π‘₯π‘₯π‘₯π‘₯ 𝑒𝑒π‘₯π‘₯π‘₯π‘₯ NOUN american_scientific_journal-4118 26 32 , , PUNCT american_scientific_journal-4118 26 33 … … PUNCT american_scientific_journal-4118 26 34 … … PUNCT american_scientific_journal-4118 26 35 … … PUNCT american_scientific_journal-4118 26 36 ) ) PUNCT american_scientific_journal-4118 27 1 = = SYM american_scientific_journal-4118 27 2 0 0 PUNCT american_scientific_journal-4118 27 3 ( ( PUNCT american_scientific_journal-4118 27 4 2.1 2.1 NUM american_scientific_journal-4118 27 5 ) ) PUNCT american_scientific_journal-4118 27 6 where where SCONJ american_scientific_journal-4118 27 7 ) ) PUNCT american_scientific_journal-4118 27 8 , , PUNCT american_scientific_journal-4118 27 9 ( ( PUNCT american_scientific_journal-4118 27 10 txuu txuu VERB american_scientific_journal-4118 27 11 = = PRON american_scientific_journal-4118 27 12 is be AUX american_scientific_journal-4118 27 13 an an DET american_scientific_journal-4118 27 14 unknown unknown ADJ american_scientific_journal-4118 27 15 function function NOUN american_scientific_journal-4118 27 16 , , PUNCT american_scientific_journal-4118 27 17 p p NOUN american_scientific_journal-4118 27 18 is be AUX american_scientific_journal-4118 27 19 a a DET american_scientific_journal-4118 27 20 polynomial polynomial NOUN american_scientific_journal-4118 27 21 in in ADP american_scientific_journal-4118 27 22 ) ) PUNCT american_scientific_journal-4118 27 23 , , PUNCT american_scientific_journal-4118 27 24 ( ( PUNCT american_scientific_journal-4118 27 25 txuu txuu NOUN american_scientific_journal-4118 27 26 = = SYM american_scientific_journal-4118 27 27 and and CCONJ american_scientific_journal-4118 27 28 its its PRON american_scientific_journal-4118 27 29 various various ADJ american_scientific_journal-4118 27 30 partial partial ADJ american_scientific_journal-4118 27 31 derivatives derivative NOUN american_scientific_journal-4118 27 32 , , PUNCT american_scientific_journal-4118 27 33 the the DET american_scientific_journal-4118 27 34 highest high ADJ american_scientific_journal-4118 27 35 order order NOUN american_scientific_journal-4118 27 36 derivatives derivative NOUN american_scientific_journal-4118 27 37 and and CCONJ american_scientific_journal-4118 27 38 nonlinear nonlinear ADJ american_scientific_journal-4118 27 39 terms term NOUN american_scientific_journal-4118 27 40 are be AUX american_scientific_journal-4118 27 41 involved involve VERB american_scientific_journal-4118 27 42 . . PUNCT american_scientific_journal-4118 28 1 the the DET american_scientific_journal-4118 28 2 outline outline NOUN american_scientific_journal-4118 28 3 of of ADP american_scientific_journal-4118 28 4 the the DET american_scientific_journal-4118 28 5 method method NOUN american_scientific_journal-4118 28 6 is be AUX american_scientific_journal-4118 28 7 given give VERB american_scientific_journal-4118 28 8 below below ADP american_scientific_journal-4118 28 9 : : PUNCT american_scientific_journal-4118 28 10 step-1 step-1 NUM american_scientific_journal-4118 28 11 : : PUNCT american_scientific_journal-4118 28 12 combine combine VERB american_scientific_journal-4118 28 13 the the DET american_scientific_journal-4118 28 14 independent independent ADJ american_scientific_journal-4118 28 15 variables variable NOUN american_scientific_journal-4118 28 16 x x PUNCT american_scientific_journal-4118 28 17 and and CCONJ american_scientific_journal-4118 28 18 t t X american_scientific_journal-4118 28 19 into into ADP american_scientific_journal-4118 28 20 one one NUM american_scientific_journal-4118 28 21 variable variable NOUN american_scientific_journal-4118 28 22 ΞΎ ΞΎ PROPN american_scientific_journal-4118 28 23 , , PUNCT american_scientific_journal-4118 28 24 by by ADP american_scientific_journal-4118 28 25 choosing choose VERB american_scientific_journal-4118 28 26 ) ) PUNCT american_scientific_journal-4118 28 27 , , PUNCT american_scientific_journal-4118 28 28 ( ( PUNCT american_scientific_journal-4118 28 29 ) ) PUNCT american_scientific_journal-4118 28 30 , , PUNCT american_scientific_journal-4118 28 31 ( ( PUNCT american_scientific_journal-4118 28 32 ΞΎutxu ΞΎutxu NOUN american_scientific_journal-4118 28 33 = = PUNCT american_scientific_journal-4118 28 34 where where SCONJ american_scientific_journal-4118 28 35 tcx tcx PROPN american_scientific_journal-4118 28 36 βˆ’=ΞΎ βˆ’=ΞΎ X american_scientific_journal-4118 28 37 ( ( PUNCT american_scientific_journal-4118 28 38 2.2 2.2 NUM american_scientific_journal-4118 28 39 ) ) PUNCT american_scientific_journal-4118 28 40 the the DET american_scientific_journal-4118 28 41 traveling travel VERB american_scientific_journal-4118 28 42 wave wave NOUN american_scientific_journal-4118 28 43 transformation transformation NOUN american_scientific_journal-4118 28 44 ( ( PUNCT american_scientific_journal-4118 28 45 2.2 2.2 NUM american_scientific_journal-4118 28 46 ) ) PUNCT american_scientific_journal-4118 28 47 permits permit VERB american_scientific_journal-4118 28 48 us we PRON american_scientific_journal-4118 28 49 to to PART american_scientific_journal-4118 28 50 transform transform VERB american_scientific_journal-4118 28 51 equation equation NOUN american_scientific_journal-4118 28 52 ( ( PUNCT american_scientific_journal-4118 28 53 2 2 NUM american_scientific_journal-4118 28 54 . . NOUN american_scientific_journal-4118 28 55 1 1 NUM american_scientific_journal-4118 28 56 ) ) PUNCT american_scientific_journal-4118 28 57 to to ADP american_scientific_journal-4118 28 58 the the DET american_scientific_journal-4118 28 59 following following ADJ american_scientific_journal-4118 28 60 ode ode PROPN american_scientific_journal-4118 28 61 : : PUNCT american_scientific_journal-4118 28 62 american american ADJ american_scientific_journal-4118 28 63 scientific scientific ADJ american_scientific_journal-4118 28 64 research research PROPN american_scientific_journal-4118 28 65 journal journal NOUN american_scientific_journal-4118 28 66 for for ADP american_scientific_journal-4118 28 67 engineering engineering NOUN american_scientific_journal-4118 28 68 , , PUNCT american_scientific_journal-4118 28 69 technology technology NOUN american_scientific_journal-4118 28 70 , , PUNCT american_scientific_journal-4118 28 71 and and CCONJ american_scientific_journal-4118 28 72 sciences science NOUN american_scientific_journal-4118 28 73 ( ( PUNCT american_scientific_journal-4118 28 74 asrjets asrjet NOUN american_scientific_journal-4118 28 75 ) ) PUNCT american_scientific_journal-4118 28 76 ( ( PUNCT american_scientific_journal-4118 28 77 2018 2018 NUM american_scientific_journal-4118 28 78 ) ) PUNCT american_scientific_journal-4118 28 79 volume volume NOUN american_scientific_journal-4118 28 80 44 44 NUM american_scientific_journal-4118 28 81 , , PUNCT american_scientific_journal-4118 28 82 no no DET american_scientific_journal-4118 28 83 1 1 NUM american_scientific_journal-4118 28 84 , , PUNCT american_scientific_journal-4118 28 85 pp pp ADV american_scientific_journal-4118 28 86 58 58 NUM american_scientific_journal-4118 28 87 - - SYM american_scientific_journal-4118 28 88 67 67 NUM american_scientific_journal-4118 28 89 60 60 NUM american_scientific_journal-4118 28 90 , , PUNCT american_scientific_journal-4118 28 91 0 0 NUM american_scientific_journal-4118 28 92 ) ) PUNCT american_scientific_journal-4118 28 93 , , PUNCT american_scientific_journal-4118 28 94 , , PUNCT american_scientific_journal-4118 28 95 , , PUNCT american_scientific_journal-4118 28 96 , , PUNCT american_scientific_journal-4118 28 97 , , PUNCT american_scientific_journal-4118 28 98 , , PUNCT american_scientific_journal-4118 28 99 ( ( PUNCT american_scientific_journal-4118 28 100 2 2 NUM american_scientific_journal-4118 28 101 = = NOUN american_scientific_journal-4118 28 102 β€²β€²β€²β€²βˆ’β€²β€²β€²β€²βˆ’ β€²β€²β€²β€²βˆ’β€²β€²β€²β€²βˆ’ NOUN american_scientific_journal-4118 28 103 llluucucuucup llluucucuucup NOUN american_scientific_journal-4118 28 104 ( ( PUNCT american_scientific_journal-4118 28 105 2.3 2.3 NUM american_scientific_journal-4118 28 106 ) ) PUNCT american_scientific_journal-4118 28 107 where where SCONJ american_scientific_journal-4118 28 108 the the DET american_scientific_journal-4118 28 109 prime prime ADJ american_scientific_journal-4118 28 110 denotes denote VERB american_scientific_journal-4118 28 111 the the DET american_scientific_journal-4118 28 112 differential differential NOUN american_scientific_journal-4118 28 113 with with ADP american_scientific_journal-4118 28 114 respect respect NOUN american_scientific_journal-4118 28 115 to to ADP american_scientific_journal-4118 28 116 πœ‰πœ‰. πœ‰πœ‰. PROPN american_scientific_journal-4118 28 117 step-2 step-2 NUM american_scientific_journal-4118 28 118 : : PUNCT american_scientific_journal-4118 28 119 we we PRON american_scientific_journal-4118 28 120 suppose suppose VERB american_scientific_journal-4118 28 121 that that SCONJ american_scientific_journal-4118 28 122 equation equation NOUN american_scientific_journal-4118 28 123 ( ( PUNCT american_scientific_journal-4118 28 124 2 2 NUM american_scientific_journal-4118 28 125 . . NOUN american_scientific_journal-4118 28 126 3 3 NUM american_scientific_journal-4118 28 127 ) ) PUNCT american_scientific_journal-4118 28 128 has have VERB american_scientific_journal-4118 28 129 the the DET american_scientific_journal-4118 28 130 solution solution NOUN american_scientific_journal-4118 28 131 of of ADP american_scientific_journal-4118 28 132 the the DET american_scientific_journal-4118 28 133 form form NOUN american_scientific_journal-4118 28 134 in in ADP american_scientific_journal-4118 28 135 the the DET american_scientific_journal-4118 28 136 finite finite ADJ american_scientific_journal-4118 28 137 series series NOUN american_scientific_journal-4118 28 138 : : PUNCT american_scientific_journal-4118 28 139 ) ) PUNCT american_scientific_journal-4118 28 140 ( ( PUNCT american_scientific_journal-4118 28 141 , , PUNCT american_scientific_journal-4118 28 142 ) ) PUNCT american_scientific_journal-4118 28 143 ( ( PUNCT american_scientific_journal-4118 28 144 0 0 NUM american_scientific_journal-4118 28 145 ΞΎΞΎ ΞΎΞΎ NOUN american_scientific_journal-4118 28 146 hhhau hhhau NOUN american_scientific_journal-4118 28 147 i i PRON american_scientific_journal-4118 28 148 m m VERB american_scientific_journal-4118 29 1 i i INTJ american_scientific_journal-4118 29 2 i i PRON american_scientific_journal-4118 30 1 = = AUX american_scientific_journal-4118 30 2 = = SYM american_scientific_journal-4118 30 3 βˆ‘ βˆ‘ PUNCT american_scientific_journal-4118 30 4 = = SYM american_scientific_journal-4118 30 5 ( ( PUNCT american_scientific_journal-4118 30 6 2.4 2.4 NUM american_scientific_journal-4118 30 7 ) ) PUNCT american_scientific_journal-4118 30 8 where where SCONJ american_scientific_journal-4118 30 9 0 0 NUM american_scientific_journal-4118 30 10 , , PUNCT american_scientific_journal-4118 30 11 β‰ mi β‰ mi VERB american_scientific_journal-4118 30 12 aa aa PROPN american_scientific_journal-4118 30 13 are be AUX american_scientific_journal-4118 30 14 constants constant NOUN american_scientific_journal-4118 30 15 to to PART american_scientific_journal-4118 30 16 be be AUX american_scientific_journal-4118 30 17 determined determine VERB american_scientific_journal-4118 30 18 , , PUNCT american_scientific_journal-4118 30 19 the the DET american_scientific_journal-4118 30 20 positive positive ADJ american_scientific_journal-4118 30 21 integer integer NOUN american_scientific_journal-4118 30 22 m m VERB american_scientific_journal-4118 30 23 can can AUX american_scientific_journal-4118 30 24 be be AUX american_scientific_journal-4118 30 25 determined determine VERB american_scientific_journal-4118 30 26 by by ADP american_scientific_journal-4118 30 27 considering consider VERB american_scientific_journal-4118 30 28 the the DET american_scientific_journal-4118 30 29 homogeneous homogeneous ADJ american_scientific_journal-4118 30 30 balance balance NOUN american_scientific_journal-4118 30 31 between between ADP american_scientific_journal-4118 30 32 the the DET american_scientific_journal-4118 30 33 highest high ADJ american_scientific_journal-4118 30 34 order order NOUN american_scientific_journal-4118 30 35 derivatives derivative NOUN american_scientific_journal-4118 30 36 and and CCONJ american_scientific_journal-4118 30 37 the the DET american_scientific_journal-4118 30 38 nonlinear nonlinear ADJ american_scientific_journal-4118 30 39 terms term NOUN american_scientific_journal-4118 30 40 appearing appear VERB american_scientific_journal-4118 30 41 in in ADP american_scientific_journal-4118 30 42 equation equation NOUN american_scientific_journal-4118 30 43 ( ( PUNCT american_scientific_journal-4118 30 44 2.3 2.3 NUM american_scientific_journal-4118 30 45 ) ) PUNCT american_scientific_journal-4118 30 46 , , PUNCT american_scientific_journal-4118 30 47 and and CCONJ american_scientific_journal-4118 30 48 ( ( PUNCT american_scientific_journal-4118 30 49 ) ) PUNCT american_scientific_journal-4118 30 50 ΞΎhh ΞΎhh NOUN american_scientific_journal-4118 30 51 = = NOUN american_scientific_journal-4118 30 52 satisfies satisfy VERB american_scientific_journal-4118 30 53 the the DET american_scientific_journal-4118 30 54 equation equation NOUN american_scientific_journal-4118 30 55 : : PUNCT american_scientific_journal-4118 30 56 , , PUNCT american_scientific_journal-4118 30 57 0 0 NUM american_scientific_journal-4118 30 58 ) ) PUNCT american_scientific_journal-4118 30 59 ) ) PUNCT american_scientific_journal-4118 31 1 ( ( PUNCT american_scientific_journal-4118 31 2 ( ( PUNCT american_scientific_journal-4118 31 3 ) ) PUNCT american_scientific_journal-4118 31 4 ( ( PUNCT american_scientific_journal-4118 31 5 = = NOUN american_scientific_journal-4118 31 6 Β±β€² Β±β€² X american_scientific_journal-4118 31 7 nhh nhh NOUN american_scientific_journal-4118 31 8 ΞΎΞΎ ΞΎΞΎ ADP american_scientific_journal-4118 31 9 where where SCONJ american_scientific_journal-4118 31 10 2β‰₯n 2β‰₯n NUM american_scientific_journal-4118 31 11 ( ( PUNCT american_scientific_journal-4118 31 12 2.5 2.5 NUM american_scientific_journal-4118 31 13 ) ) PUNCT american_scientific_journal-4118 32 1 step-3 step-3 NOUN american_scientific_journal-4118 32 2 : : PUNCT american_scientific_journal-4118 32 3 we we PRON american_scientific_journal-4118 32 4 substitute substitute VERB american_scientific_journal-4118 32 5 equation equation NOUN american_scientific_journal-4118 32 6 ( ( PUNCT american_scientific_journal-4118 32 7 2.4 2.4 NUM american_scientific_journal-4118 32 8 ) ) PUNCT american_scientific_journal-4118 32 9 into into ADP american_scientific_journal-4118 32 10 equation equation NOUN american_scientific_journal-4118 32 11 ( ( PUNCT american_scientific_journal-4118 32 12 2.3 2.3 NUM american_scientific_journal-4118 32 13 ) ) PUNCT american_scientific_journal-4118 32 14 and and CCONJ american_scientific_journal-4118 32 15 use use VERB american_scientific_journal-4118 32 16 equation equation NOUN american_scientific_journal-4118 32 17 ( ( PUNCT american_scientific_journal-4118 32 18 2.5 2.5 NUM american_scientific_journal-4118 32 19 ) ) PUNCT american_scientific_journal-4118 32 20 and and CCONJ american_scientific_journal-4118 32 21 then then ADV american_scientific_journal-4118 32 22 we we PRON american_scientific_journal-4118 32 23 account account VERB american_scientific_journal-4118 32 24 the the DET american_scientific_journal-4118 32 25 function function NOUN american_scientific_journal-4118 32 26 h(ΞΎ h(ΞΎ NOUN american_scientific_journal-4118 32 27 ) ) PUNCT american_scientific_journal-4118 32 28 . . PUNCT american_scientific_journal-4118 33 1 as as ADP american_scientific_journal-4118 33 2 a a DET american_scientific_journal-4118 33 3 result result NOUN american_scientific_journal-4118 33 4 of of ADP american_scientific_journal-4118 33 5 this this DET american_scientific_journal-4118 33 6 substitution substitution NOUN american_scientific_journal-4118 33 7 , , PUNCT american_scientific_journal-4118 33 8 we we PRON american_scientific_journal-4118 33 9 get get VERB american_scientific_journal-4118 33 10 a a DET american_scientific_journal-4118 33 11 polynomial polynomial NOUN american_scientific_journal-4118 33 12 of of ADP american_scientific_journal-4118 33 13 h(ΞΎ h(ΞΎ NOUN american_scientific_journal-4118 33 14 ) ) PUNCT american_scientific_journal-4118 33 15 . . PUNCT american_scientific_journal-4118 34 1 we we PRON american_scientific_journal-4118 34 2 equate equate VERB american_scientific_journal-4118 34 3 all all DET american_scientific_journal-4118 34 4 the the DET american_scientific_journal-4118 34 5 coefficients coefficient NOUN american_scientific_journal-4118 34 6 of of ADP american_scientific_journal-4118 34 7 same same ADJ american_scientific_journal-4118 34 8 power power NOUN american_scientific_journal-4118 34 9 of of ADP american_scientific_journal-4118 34 10 h(ΞΎ h(ΞΎ NOUN american_scientific_journal-4118 34 11 ) ) PUNCT american_scientific_journal-4118 34 12 to to ADP american_scientific_journal-4118 34 13 zero zero NUM american_scientific_journal-4118 34 14 . . PUNCT american_scientific_journal-4118 35 1 this this DET american_scientific_journal-4118 35 2 procedure procedure NOUN american_scientific_journal-4118 35 3 yields yield VERB american_scientific_journal-4118 35 4 a a DET american_scientific_journal-4118 35 5 system system NOUN american_scientific_journal-4118 35 6 of of ADP american_scientific_journal-4118 35 7 algebraic algebraic ADJ american_scientific_journal-4118 35 8 equations equation NOUN american_scientific_journal-4118 35 9 whichever whichever PRON american_scientific_journal-4118 35 10 can can AUX american_scientific_journal-4118 35 11 be be AUX american_scientific_journal-4118 35 12 solved solve VERB american_scientific_journal-4118 35 13 to to PART american_scientific_journal-4118 35 14 find find VERB american_scientific_journal-4118 35 15 ia ia PROPN american_scientific_journal-4118 35 16 . . PUNCT american_scientific_journal-4118 36 1 step-4 step-4 NUM american_scientific_journal-4118 36 2 : : PUNCT american_scientific_journal-4118 36 3 substituting substitute VERB american_scientific_journal-4118 36 4 the the DET american_scientific_journal-4118 36 5 values value NOUN american_scientific_journal-4118 36 6 ia ia PROPN american_scientific_journal-4118 36 7 into into ADP american_scientific_journal-4118 36 8 equation equation NOUN american_scientific_journal-4118 36 9 ( ( PUNCT american_scientific_journal-4118 36 10 2.4 2.4 NUM american_scientific_journal-4118 36 11 ) ) PUNCT american_scientific_journal-4118 36 12 along along ADP american_scientific_journal-4118 36 13 with with ADP american_scientific_journal-4118 36 14 general general ADJ american_scientific_journal-4118 36 15 solutions solution NOUN american_scientific_journal-4118 36 16 of of ADP american_scientific_journal-4118 36 17 equation equation NOUN american_scientific_journal-4118 36 18 ( ( PUNCT american_scientific_journal-4118 36 19 2.5 2.5 NUM american_scientific_journal-4118 36 20 ) ) PUNCT american_scientific_journal-4118 36 21 complete complete VERB american_scientific_journal-4118 36 22 the the DET american_scientific_journal-4118 36 23 determination determination NOUN american_scientific_journal-4118 36 24 of of ADP american_scientific_journal-4118 36 25 the the DET american_scientific_journal-4118 36 26 solution solution NOUN american_scientific_journal-4118 36 27 of of ADP american_scientific_journal-4118 36 28 equation equation NOUN american_scientific_journal-4118 36 29 ( ( PUNCT american_scientific_journal-4118 36 30 2.1).finally 2.1).finally ADV american_scientific_journal-4118 36 31 particular particular ADJ american_scientific_journal-4118 36 32 choice choice NOUN american_scientific_journal-4118 36 33 of of ADP american_scientific_journal-4118 36 34 unknown unknown ADJ american_scientific_journal-4118 36 35 parameters parameter NOUN american_scientific_journal-4118 36 36 in in ADP american_scientific_journal-4118 36 37 exact exact ADJ american_scientific_journal-4118 36 38 solutions solution NOUN american_scientific_journal-4118 36 39 gives give VERB american_scientific_journal-4118 36 40 the the DET american_scientific_journal-4118 36 41 desired desire VERB american_scientific_journal-4118 36 42 solitary solitary ADJ american_scientific_journal-4118 36 43 wave wave NOUN american_scientific_journal-4118 36 44 solutions solution NOUN american_scientific_journal-4118 36 45 . . PUNCT american_scientific_journal-4118 37 1 3 3 X american_scientific_journal-4118 37 2 . . X american_scientific_journal-4118 37 3 applications application NOUN american_scientific_journal-4118 37 4 of of ADP american_scientific_journal-4118 37 5 the the DET american_scientific_journal-4118 37 6 method method NOUN american_scientific_journal-4118 37 7 to to PART american_scientific_journal-4118 37 8 illustrate illustrate VERB american_scientific_journal-4118 37 9 the the DET american_scientific_journal-4118 37 10 idea idea NOUN american_scientific_journal-4118 37 11 of of ADP american_scientific_journal-4118 37 12 the the DET american_scientific_journal-4118 37 13 proposed propose VERB american_scientific_journal-4118 37 14 method method NOUN american_scientific_journal-4118 37 15 , , PUNCT american_scientific_journal-4118 37 16 we we PRON american_scientific_journal-4118 37 17 have have AUX american_scientific_journal-4118 37 18 selected select VERB american_scientific_journal-4118 37 19 two two NUM american_scientific_journal-4118 37 20 nonlinear nonlinear ADJ american_scientific_journal-4118 37 21 pdes pde NOUN american_scientific_journal-4118 37 22 , , PUNCT american_scientific_journal-4118 37 23 such such ADJ american_scientific_journal-4118 37 24 as as ADP american_scientific_journal-4118 37 25 the the DET american_scientific_journal-4118 37 26 modified modify VERB american_scientific_journal-4118 37 27 liouville liouville NOUN american_scientific_journal-4118 37 28 equation equation NOUN american_scientific_journal-4118 37 29 and and CCONJ american_scientific_journal-4118 37 30 the the DET american_scientific_journal-4118 37 31 regularized regularize VERB american_scientific_journal-4118 37 32 long long ADJ american_scientific_journal-4118 37 33 wave wave NOUN american_scientific_journal-4118 37 34 equation equation NOUN american_scientific_journal-4118 37 35 which which PRON american_scientific_journal-4118 37 36 arise arise VERB american_scientific_journal-4118 37 37 in in ADP american_scientific_journal-4118 37 38 mathematical mathematical ADJ american_scientific_journal-4118 37 39 physics physics NOUN american_scientific_journal-4118 37 40 . . PUNCT american_scientific_journal-4118 38 1 example-1 example-1 NOUN american_scientific_journal-4118 38 2 : : PUNCT american_scientific_journal-4118 38 3 solution solution NOUN american_scientific_journal-4118 38 4 of of ADP american_scientific_journal-4118 38 5 modified modify VERB american_scientific_journal-4118 38 6 liouville liouville NOUN american_scientific_journal-4118 38 7 equation equation NOUN american_scientific_journal-4118 38 8 𝑀𝑀𝑑𝑑𝑑𝑑 𝑀𝑀𝑑𝑑𝑑𝑑 VERB american_scientific_journal-4118 38 9 = = PUNCT american_scientific_journal-4118 38 10 π‘Žπ‘Ž2𝑀𝑀π‘₯π‘₯π‘₯π‘₯ π‘Žπ‘Ž2𝑀𝑀π‘₯π‘₯π‘₯π‘₯ PUNCT american_scientific_journal-4118 39 1 + + NUM american_scientific_journal-4118 39 2 𝑏𝑏𝑒𝑒𝛽𝛽𝛽𝛽 𝑏𝑏𝑒𝑒𝛽𝛽𝛽𝛽 NOUN american_scientific_journal-4118 39 3 ( ( PUNCT american_scientific_journal-4118 39 4 3.1 3.1 NUM american_scientific_journal-4118 39 5 ) ) PUNCT american_scientific_journal-4118 39 6 that that PRON american_scientific_journal-4118 39 7 arises arise VERB american_scientific_journal-4118 39 8 in in ADP american_scientific_journal-4118 39 9 hydrodynamics hydrodynamic NOUN american_scientific_journal-4118 39 10 , , PUNCT american_scientific_journal-4118 39 11 where where SCONJ american_scientific_journal-4118 39 12 w(x w(x PROPN american_scientific_journal-4118 39 13 , , PUNCT american_scientific_journal-4118 39 14 t t PROPN american_scientific_journal-4118 39 15 ) ) PUNCT american_scientific_journal-4118 39 16 is be AUX american_scientific_journal-4118 39 17 the the DET american_scientific_journal-4118 39 18 stream stream NOUN american_scientific_journal-4118 39 19 function function NOUN american_scientific_journal-4118 39 20 and and CCONJ american_scientific_journal-4118 39 21 a a DET american_scientific_journal-4118 39 22 , , PUNCT american_scientific_journal-4118 39 23 b b NOUN american_scientific_journal-4118 39 24 , , PUNCT american_scientific_journal-4118 39 25 Ξ² Ξ² X american_scientific_journal-4118 39 26 are be AUX american_scientific_journal-4118 39 27 nonzero nonzero PROPN american_scientific_journal-4118 39 28 constants[23 constants[23 PROPN american_scientific_journal-4118 39 29 - - PUNCT american_scientific_journal-4118 39 30 24 24 NUM american_scientific_journal-4118 39 31 ] ] PUNCT american_scientific_journal-4118 39 32 . . PUNCT american_scientific_journal-4118 40 1 we we PRON american_scientific_journal-4118 40 2 first first ADV american_scientific_journal-4118 40 3 use use VERB american_scientific_journal-4118 40 4 the the DET american_scientific_journal-4118 40 5 painleve painleve NOUN american_scientific_journal-4118 40 6 transformation transformation NOUN american_scientific_journal-4118 40 7 ( ( PUNCT american_scientific_journal-4118 40 8 ) ) PUNCT american_scientific_journal-4118 40 9 wetxu wetxu VERB american_scientific_journal-4118 40 10 Ξ²= Ξ²= NOUN american_scientific_journal-4118 40 11 , , PUNCT american_scientific_journal-4118 40 12 , , PUNCT american_scientific_journal-4118 40 13 so so SCONJ american_scientific_journal-4118 40 14 that that SCONJ american_scientific_journal-4118 40 15 𝑀𝑀 𝑀𝑀 NOUN american_scientific_journal-4118 40 16 = = SYM american_scientific_journal-4118 40 17 1 1 NUM american_scientific_journal-4118 40 18 𝛽𝛽 𝛽𝛽 ADP american_scientific_journal-4118 40 19 𝑙𝑙𝑙𝑙𝑒𝑒. 𝑙𝑙𝑙𝑙𝑒𝑒. NOUN american_scientific_journal-4118 40 20 ( ( PUNCT american_scientific_journal-4118 40 21 3.2 3.2 NUM american_scientific_journal-4118 40 22 ) ) PUNCT american_scientific_journal-4118 40 23 now now ADV american_scientific_journal-4118 40 24 the the DET american_scientific_journal-4118 40 25 wave wave NOUN american_scientific_journal-4118 40 26 transformation transformation NOUN american_scientific_journal-4118 40 27 equations equations PROPN american_scientific_journal-4118 40 28 𝑒𝑒(π‘₯π‘₯ 𝑒𝑒(π‘₯π‘₯ PROPN american_scientific_journal-4118 40 29 , , PUNCT american_scientific_journal-4118 40 30 𝑑𝑑 𝑑𝑑 ADJ american_scientific_journal-4118 40 31 ) ) PUNCT american_scientific_journal-4118 40 32 = = SYM american_scientific_journal-4118 40 33 𝑒𝑒(πœ‰πœ‰ 𝑒𝑒(πœ‰πœ‰ NOUN american_scientific_journal-4118 40 34 ) ) PUNCT american_scientific_journal-4118 40 35 , , PUNCT american_scientific_journal-4118 40 36 πœ‰πœ‰ πœ‰πœ‰ PROPN american_scientific_journal-4118 40 37 = = PUNCT american_scientific_journal-4118 40 38 π‘₯π‘₯ π‘₯π‘₯ ADP american_scientific_journal-4118 40 39 βˆ’ βˆ’ PROPN american_scientific_journal-4118 40 40 𝑐𝑐𝑑𝑑 𝑐𝑐𝑑𝑑 NOUN american_scientific_journal-4118 40 41 and and CCONJ american_scientific_journal-4118 40 42 equation equation NOUN american_scientific_journal-4118 40 43 ( ( PUNCT american_scientific_journal-4118 40 44 3.2 3.2 NUM american_scientific_journal-4118 40 45 ) ) PUNCT american_scientific_journal-4118 40 46 reduces reduce VERB american_scientific_journal-4118 40 47 equation equation NOUN american_scientific_journal-4118 40 48 ( ( PUNCT american_scientific_journal-4118 40 49 3.1 3.1 NUM american_scientific_journal-4118 40 50 ) ) PUNCT american_scientific_journal-4118 40 51 into into ADP american_scientific_journal-4118 40 52 the the DET american_scientific_journal-4118 40 53 following following ADJ american_scientific_journal-4118 40 54 ode ode PROPN american_scientific_journal-4118 40 55 : : PUNCT american_scientific_journal-4118 40 56 american american ADJ american_scientific_journal-4118 40 57 scientific scientific ADJ american_scientific_journal-4118 40 58 research research PROPN american_scientific_journal-4118 40 59 journal journal NOUN american_scientific_journal-4118 40 60 for for ADP american_scientific_journal-4118 40 61 engineering engineering NOUN american_scientific_journal-4118 40 62 , , PUNCT american_scientific_journal-4118 40 63 technology technology NOUN american_scientific_journal-4118 40 64 , , PUNCT american_scientific_journal-4118 40 65 and and CCONJ american_scientific_journal-4118 40 66 sciences science NOUN american_scientific_journal-4118 40 67 ( ( PUNCT american_scientific_journal-4118 40 68 asrjets asrjet NOUN american_scientific_journal-4118 40 69 ) ) PUNCT american_scientific_journal-4118 40 70 ( ( PUNCT american_scientific_journal-4118 40 71 2018 2018 NUM american_scientific_journal-4118 40 72 ) ) PUNCT american_scientific_journal-4118 40 73 volume volume NOUN american_scientific_journal-4118 40 74 44 44 NUM american_scientific_journal-4118 40 75 , , PUNCT american_scientific_journal-4118 40 76 no no DET american_scientific_journal-4118 40 77 1 1 NUM american_scientific_journal-4118 40 78 , , PUNCT american_scientific_journal-4118 40 79 pp pp ADV american_scientific_journal-4118 40 80 58 58 NUM american_scientific_journal-4118 40 81 - - SYM american_scientific_journal-4118 40 82 67 67 NUM american_scientific_journal-4118 40 83 61 61 NUM american_scientific_journal-4118 40 84 032 032 NUM american_scientific_journal-4118 41 1 = = PUNCT american_scientific_journal-4118 41 2 + + NOUN american_scientific_journal-4118 41 3 β€²βˆ’β€²β€² β€²βˆ’β€²β€² NOUN american_scientific_journal-4118 41 4 kuuuu kuuuu VERB american_scientific_journal-4118 41 5 where where SCONJ american_scientific_journal-4118 41 6 22 22 NUM american_scientific_journal-4118 41 7 ca ca AUX american_scientific_journal-4118 41 8 bk bk VERB american_scientific_journal-4118 41 9 βˆ’ βˆ’ NOUN american_scientific_journal-4118 41 10 = = SYM american_scientific_journal-4118 41 11 Ξ² Ξ² X american_scientific_journal-4118 41 12 and and CCONJ american_scientific_journal-4118 41 13 ac ac PROPN american_scientific_journal-4118 41 14 Β±β‰  Β±β‰  PUNCT american_scientific_journal-4118 41 15 ( ( PUNCT american_scientific_journal-4118 41 16 3.3 3.3 NUM american_scientific_journal-4118 41 17 ) ) PUNCT american_scientific_journal-4118 41 18 let let VERB american_scientific_journal-4118 41 19 ( ( PUNCT american_scientific_journal-4118 41 20 3.3 3.3 NUM american_scientific_journal-4118 41 21 ) ) PUNCT american_scientific_journal-4118 41 22 has have VERB american_scientific_journal-4118 41 23 the the DET american_scientific_journal-4118 41 24 solution solution NOUN american_scientific_journal-4118 41 25 of of ADP american_scientific_journal-4118 41 26 the the DET american_scientific_journal-4118 41 27 form form NOUN american_scientific_journal-4118 41 28 : : PUNCT american_scientific_journal-4118 41 29 ) ) PUNCT american_scientific_journal-4118 41 30 ( ( PUNCT american_scientific_journal-4118 41 31 , , PUNCT american_scientific_journal-4118 41 32 ) ) PUNCT american_scientific_journal-4118 41 33 ( ( PUNCT american_scientific_journal-4118 41 34 0 0 NUM american_scientific_journal-4118 41 35 ΞΎΞΎ ΞΎΞΎ NOUN american_scientific_journal-4118 41 36 hhhau hhhau NOUN american_scientific_journal-4118 42 1 i i PRON american_scientific_journal-4118 42 2 m m VERB american_scientific_journal-4118 42 3 i i INTJ american_scientific_journal-4118 42 4 i i PRON american_scientific_journal-4118 42 5 = = PUNCT american_scientific_journal-4118 42 6 = = NOUN american_scientific_journal-4118 42 7 βˆ‘ βˆ‘ PUNCT american_scientific_journal-4118 42 8 = = SYM american_scientific_journal-4118 42 9 ( ( PUNCT american_scientific_journal-4118 42 10 3.4 3.4 NUM american_scientific_journal-4118 42 11 ) ) PUNCT american_scientific_journal-4118 42 12 hence hence ADV american_scientific_journal-4118 42 13 for for ADP american_scientific_journal-4118 42 14 different different ADJ american_scientific_journal-4118 42 15 for for ADP american_scientific_journal-4118 42 16 values value NOUN american_scientific_journal-4118 42 17 of of ADP american_scientific_journal-4118 42 18 n n PRON american_scientific_journal-4118 42 19 in in ADP american_scientific_journal-4118 42 20 ( ( PUNCT american_scientific_journal-4118 42 21 2.5 2.5 NUM american_scientific_journal-4118 42 22 ) ) PUNCT american_scientific_journal-4118 42 23 , , PUNCT american_scientific_journal-4118 42 24 the the DET american_scientific_journal-4118 42 25 corresponding corresponding ADJ american_scientific_journal-4118 42 26 exact exact ADJ american_scientific_journal-4118 42 27 solutions solution NOUN american_scientific_journal-4118 42 28 of of ADP american_scientific_journal-4118 42 29 ( ( PUNCT american_scientific_journal-4118 42 30 3.1 3.1 NUM american_scientific_journal-4118 42 31 ) ) PUNCT american_scientific_journal-4118 42 32 are be AUX american_scientific_journal-4118 42 33 obtained obtain VERB american_scientific_journal-4118 42 34 below below ADV american_scientific_journal-4118 42 35 : : PUNCT american_scientific_journal-4118 42 36 ( ( PUNCT american_scientific_journal-4118 42 37 a a X american_scientific_journal-4118 42 38 ) ) PUNCT american_scientific_journal-4118 42 39 2 2 NUM american_scientific_journal-4118 42 40 = = NOUN american_scientific_journal-4118 42 41 n n NUM american_scientific_journal-4118 42 42 : : PUNCT american_scientific_journal-4118 42 43 by by ADP american_scientific_journal-4118 42 44 considering consider VERB american_scientific_journal-4118 42 45 the the DET american_scientific_journal-4118 42 46 homogeneous homogeneous ADJ american_scientific_journal-4118 42 47 balance balance NOUN american_scientific_journal-4118 42 48 between between ADP american_scientific_journal-4118 42 49 𝑒𝑒′′′ 𝑒𝑒′′′ NOUN american_scientific_journal-4118 42 50 and and CCONJ american_scientific_journal-4118 42 51 𝑒𝑒𝑒𝑒′appearing 𝑒𝑒𝑒𝑒′appeare VERB american_scientific_journal-4118 42 52 in in ADP american_scientific_journal-4118 42 53 eq.(3.3 eq.(3.3 NOUN american_scientific_journal-4118 42 54 ) ) PUNCT american_scientific_journal-4118 42 55 , , PUNCT american_scientific_journal-4118 42 56 we we PRON american_scientific_journal-4118 42 57 get get VERB american_scientific_journal-4118 42 58 π‘šπ‘š π‘šπ‘š ADP american_scientific_journal-4118 42 59 = = NOUN american_scientific_journal-4118 42 60 2 2 X american_scientific_journal-4118 42 61 . . PUNCT american_scientific_journal-4118 43 1 as as ADP american_scientific_journal-4118 43 2 a a DET american_scientific_journal-4118 43 3 result result NOUN american_scientific_journal-4118 43 4 , , PUNCT american_scientific_journal-4118 43 5 ( ( PUNCT american_scientific_journal-4118 43 6 3.4 3.4 NUM american_scientific_journal-4118 43 7 ) ) PUNCT american_scientific_journal-4118 43 8 takes take VERB american_scientific_journal-4118 43 9 the the DET american_scientific_journal-4118 43 10 form form NOUN american_scientific_journal-4118 43 11 : : PUNCT american_scientific_journal-4118 43 12 2 2 NUM american_scientific_journal-4118 43 13 210 210 NUM american_scientific_journal-4118 43 14 ) ) PUNCT american_scientific_journal-4118 43 15 ( ( PUNCT american_scientific_journal-4118 43 16 hahaau hahaau PROPN american_scientific_journal-4118 43 17 + + PROPN american_scientific_journal-4118 43 18 + + PROPN american_scientific_journal-4118 43 19 = = SYM american_scientific_journal-4118 43 20 ΞΎ ΞΎ X american_scientific_journal-4118 43 21 ( ( PUNCT american_scientific_journal-4118 43 22 3.5 3.5 NUM american_scientific_journal-4118 43 23 ) ) PUNCT american_scientific_journal-4118 43 24 where where SCONJ american_scientific_journal-4118 43 25 π‘Žπ‘Ž0 π‘Žπ‘Ž0 PROPN american_scientific_journal-4118 43 26 , , PUNCT american_scientific_journal-4118 43 27 π‘Žπ‘Ž1 π‘Žπ‘Ž1 PROPN american_scientific_journal-4118 43 28 , , PUNCT american_scientific_journal-4118 43 29 π‘Žπ‘Ž2 π‘Žπ‘Ž2 X american_scientific_journal-4118 43 30 are be AUX american_scientific_journal-4118 43 31 unknown unknown ADJ american_scientific_journal-4118 43 32 constants constant NOUN american_scientific_journal-4118 43 33 to to PART american_scientific_journal-4118 43 34 be be AUX american_scientific_journal-4118 43 35 determined determine VERB american_scientific_journal-4118 43 36 and and CCONJ american_scientific_journal-4118 43 37 ) ) PUNCT american_scientific_journal-4118 43 38 ( ( PUNCT american_scientific_journal-4118 43 39 ΞΎh ΞΎh NUM american_scientific_journal-4118 43 40 satisfies satisfy VERB american_scientific_journal-4118 43 41 the the DET american_scientific_journal-4118 43 42 eq.(2.5 eq.(2.5 NOUN american_scientific_journal-4118 43 43 ) ) PUNCT american_scientific_journal-4118 43 44 and and CCONJ american_scientific_journal-4118 43 45 this this DET american_scientific_journal-4118 43 46 function function NOUN american_scientific_journal-4118 43 47 is be AUX american_scientific_journal-4118 43 48 determined determine VERB american_scientific_journal-4118 43 49 from from ADP american_scientific_journal-4118 43 50 eq eq PROPN american_scientific_journal-4118 43 51 . . PUNCT american_scientific_journal-4118 44 1 ( ( PUNCT american_scientific_journal-4118 44 2 1.1 1.1 NUM american_scientific_journal-4118 44 3 ) ) PUNCT american_scientific_journal-4118 44 4 by by ADP american_scientific_journal-4118 44 5 setting set VERB american_scientific_journal-4118 44 6 𝑙𝑙 𝑙𝑙 ADP american_scientific_journal-4118 44 7 = = ADJ american_scientific_journal-4118 44 8 2 2 X american_scientific_journal-4118 44 9 . . X american_scientific_journal-4118 45 1 substituting substitute VERB american_scientific_journal-4118 45 2 ( ( PUNCT american_scientific_journal-4118 45 3 3.5 3.5 NUM american_scientific_journal-4118 45 4 ) ) PUNCT american_scientific_journal-4118 45 5 in in ADP american_scientific_journal-4118 45 6 the the DET american_scientific_journal-4118 45 7 reduced reduce VERB american_scientific_journal-4118 45 8 ode ode NOUN american_scientific_journal-4118 45 9 ( ( PUNCT american_scientific_journal-4118 45 10 3.3 3.3 NUM american_scientific_journal-4118 45 11 ) ) PUNCT american_scientific_journal-4118 45 12 and and CCONJ american_scientific_journal-4118 45 13 collecting collect VERB american_scientific_journal-4118 45 14 the the DET american_scientific_journal-4118 45 15 coefficients coefficient NOUN american_scientific_journal-4118 45 16 of of ADP american_scientific_journal-4118 45 17 various various ADJ american_scientific_journal-4118 45 18 power power NOUN american_scientific_journal-4118 45 19 of of ADP american_scientific_journal-4118 45 20 𝐻𝐻(πœ‰πœ‰ 𝐻𝐻(πœ‰πœ‰ NOUN american_scientific_journal-4118 45 21 ) ) PUNCT american_scientific_journal-4118 45 22 yields yield VERB american_scientific_journal-4118 45 23 the the DET american_scientific_journal-4118 45 24 following follow VERB american_scientific_journal-4118 45 25 system system NOUN american_scientific_journal-4118 45 26 of of ADP american_scientific_journal-4118 45 27 algebraic algebraic ADJ american_scientific_journal-4118 45 28 equations equation NOUN american_scientific_journal-4118 45 29 . . PUNCT american_scientific_journal-4118 46 1 02 02 NUM american_scientific_journal-4118 46 2 : : SYM american_scientific_journal-4118 46 3 2 2 NUM american_scientific_journal-4118 46 4 2 2 NUM american_scientific_journal-4118 46 5 3 3 NUM american_scientific_journal-4118 46 6 2 2 NUM american_scientific_journal-4118 46 7 6 6 NUM american_scientific_journal-4118 46 8 = = NOUN american_scientific_journal-4118 46 9 + + NUM american_scientific_journal-4118 46 10 akah akah NOUN american_scientific_journal-4118 46 11 034 034 NUM american_scientific_journal-4118 46 12 : : PUNCT american_scientific_journal-4118 46 13 2 2 NUM american_scientific_journal-4118 46 14 2121 2121 NUM american_scientific_journal-4118 46 15 5 5 NUM american_scientific_journal-4118 46 16 = = SYM american_scientific_journal-4118 46 17 + + NOUN american_scientific_journal-4118 46 18 akaaah akaaah ADJ american_scientific_journal-4118 46 19 0363 0363 NUM american_scientific_journal-4118 46 20 : : PUNCT american_scientific_journal-4118 46 21 2 2 NUM american_scientific_journal-4118 46 22 20202 20202 NUM american_scientific_journal-4118 46 23 2 2 NUM american_scientific_journal-4118 46 24 1 1 NUM american_scientific_journal-4118 46 25 2 2 NUM american_scientific_journal-4118 46 26 1 1 NUM american_scientific_journal-4118 46 27 4 4 NUM american_scientific_journal-4118 46 28 = = NOUN american_scientific_journal-4118 46 29 + + NOUN american_scientific_journal-4118 46 30 + + ADJ american_scientific_journal-4118 46 31 + + CCONJ american_scientific_journal-4118 46 32 akaaaakaah akaaaakaah ADJ american_scientific_journal-4118 46 33 062 062 NUM american_scientific_journal-4118 46 34 : : PUNCT american_scientific_journal-4118 46 35 3 3 NUM american_scientific_journal-4118 46 36 121010 121010 NUM american_scientific_journal-4118 46 37 3 3 NUM american_scientific_journal-4118 46 38 = = SYM american_scientific_journal-4118 46 39 + + NOUN american_scientific_journal-4118 46 40 + + ADJ american_scientific_journal-4118 46 41 kaaakaaah kaaakaaah ADJ american_scientific_journal-4118 46 42 033 033 NUM american_scientific_journal-4118 46 43 : : SYM american_scientific_journal-4118 46 44 2 2 NUM american_scientific_journal-4118 46 45 2 2 NUM american_scientific_journal-4118 46 46 0 0 NUM american_scientific_journal-4118 46 47 2 2 NUM american_scientific_journal-4118 46 48 10 10 NUM american_scientific_journal-4118 46 49 2 2 NUM american_scientific_journal-4118 46 50 = = SYM american_scientific_journal-4118 46 51 + + NUM american_scientific_journal-4118 46 52 akaakah akaakah NOUN american_scientific_journal-4118 46 53 03 03 NUM american_scientific_journal-4118 46 54 : : PUNCT american_scientific_journal-4118 46 55 1 1 NUM american_scientific_journal-4118 46 56 2 2 NUM american_scientific_journal-4118 46 57 0 0 NUM american_scientific_journal-4118 46 58 1 1 NUM american_scientific_journal-4118 46 59 = = NOUN american_scientific_journal-4118 46 60 akah akah NOUN american_scientific_journal-4118 46 61 0 0 NUM american_scientific_journal-4118 46 62 : : PUNCT american_scientific_journal-4118 46 63 3 3 NUM american_scientific_journal-4118 46 64 0 0 NUM american_scientific_journal-4118 46 65 0 0 NUM american_scientific_journal-4118 47 1 = = SYM american_scientific_journal-4118 47 2 kah kah PROPN american_scientific_journal-4118 47 3 solving solve VERB american_scientific_journal-4118 47 4 the the DET american_scientific_journal-4118 47 5 above above ADJ american_scientific_journal-4118 47 6 equations equation NOUN american_scientific_journal-4118 47 7 , , PUNCT american_scientific_journal-4118 47 8 we we PRON american_scientific_journal-4118 47 9 get get VERB american_scientific_journal-4118 47 10 .2,0,0 .2,0,0 NOUN american_scientific_journal-4118 47 11 210 210 NUM american_scientific_journal-4118 47 12 k k NOUN american_scientific_journal-4118 47 13 aaa aaa NOUN american_scientific_journal-4118 47 14 βˆ’ βˆ’ NOUN american_scientific_journal-4118 48 1 = = NOUN american_scientific_journal-4118 48 2 = = SYM american_scientific_journal-4118 48 3 = = X american_scientific_journal-4118 48 4 ( ( PUNCT american_scientific_journal-4118 48 5 3.6 3.6 NUM american_scientific_journal-4118 48 6 ) ) PUNCT american_scientific_journal-4118 48 7 hence hence ADV american_scientific_journal-4118 48 8 the the DET american_scientific_journal-4118 48 9 solution solution NOUN american_scientific_journal-4118 48 10 of of ADP american_scientific_journal-4118 48 11 ( ( PUNCT american_scientific_journal-4118 48 12 3.4 3.4 NUM american_scientific_journal-4118 48 13 ) ) PUNCT american_scientific_journal-4118 48 14 takes take VERB american_scientific_journal-4118 48 15 the the DET american_scientific_journal-4118 48 16 form form NOUN american_scientific_journal-4118 48 17 2 2 NUM american_scientific_journal-4118 48 18 1 1 NUM american_scientific_journal-4118 48 19 ) ) PUNCT american_scientific_journal-4118 48 20 ( ( PUNCT american_scientific_journal-4118 48 21 2 2 NUM american_scientific_journal-4118 48 22 ) ) PUNCT american_scientific_journal-4118 48 23 ( ( PUNCT american_scientific_journal-4118 48 24 ΞΎ ΞΎ PROPN american_scientific_journal-4118 48 25 ΞΎ ΞΎ PROPN american_scientific_journal-4118 48 26 Β± Β± NOUN american_scientific_journal-4118 48 27 βˆ’ βˆ’ NOUN american_scientific_journal-4118 49 1 = = SYM american_scientific_journal-4118 49 2 ck ck PROPN american_scientific_journal-4118 49 3 u u NOUN american_scientific_journal-4118 49 4 ( ( PUNCT american_scientific_journal-4118 49 5 3.7 3.7 NUM american_scientific_journal-4118 49 6 ) ) PUNCT american_scientific_journal-4118 49 7 american american ADJ american_scientific_journal-4118 49 8 scientific scientific ADJ american_scientific_journal-4118 49 9 research research NOUN american_scientific_journal-4118 49 10 journal journal NOUN american_scientific_journal-4118 49 11 for for ADP american_scientific_journal-4118 49 12 engineering engineering NOUN american_scientific_journal-4118 49 13 , , PUNCT american_scientific_journal-4118 49 14 technology technology NOUN american_scientific_journal-4118 49 15 , , PUNCT american_scientific_journal-4118 49 16 and and CCONJ american_scientific_journal-4118 49 17 sciences science NOUN american_scientific_journal-4118 49 18 ( ( PUNCT american_scientific_journal-4118 49 19 asrjets asrjet NOUN american_scientific_journal-4118 49 20 ) ) PUNCT american_scientific_journal-4118 49 21 ( ( PUNCT american_scientific_journal-4118 49 22 2018 2018 NUM american_scientific_journal-4118 49 23 ) ) PUNCT american_scientific_journal-4118 49 24 volume volume NOUN american_scientific_journal-4118 49 25 44 44 NUM american_scientific_journal-4118 49 26 , , PUNCT american_scientific_journal-4118 49 27 no no DET american_scientific_journal-4118 49 28 1 1 NUM american_scientific_journal-4118 49 29 , , PUNCT american_scientific_journal-4118 49 30 pp pp ADV american_scientific_journal-4118 49 31 58 58 NUM american_scientific_journal-4118 49 32 - - SYM american_scientific_journal-4118 49 33 67 67 NUM american_scientific_journal-4118 49 34 62 62 NUM american_scientific_journal-4118 49 35 finally finally ADV american_scientific_journal-4118 49 36 putting put VERB american_scientific_journal-4118 49 37 πœ‰πœ‰ πœ‰πœ‰ NOUN american_scientific_journal-4118 49 38 = = PUNCT american_scientific_journal-4118 49 39 π‘₯π‘₯ π‘₯π‘₯ ADP american_scientific_journal-4118 49 40 βˆ’ βˆ’ PROPN american_scientific_journal-4118 49 41 𝑐𝑐𝑑𝑑 𝑐𝑐𝑑𝑑 NOUN american_scientific_journal-4118 49 42 , , PUNCT american_scientific_journal-4118 49 43 and and CCONJ american_scientific_journal-4118 49 44 using use VERB american_scientific_journal-4118 49 45 equation equation NOUN american_scientific_journal-4118 49 46 ( ( PUNCT american_scientific_journal-4118 49 47 1.1 1.1 NUM american_scientific_journal-4118 49 48 ) ) PUNCT american_scientific_journal-4118 49 49 , , PUNCT american_scientific_journal-4118 49 50 we we PRON american_scientific_journal-4118 49 51 get get VERB american_scientific_journal-4118 49 52 the the DET american_scientific_journal-4118 49 53 following follow VERB american_scientific_journal-4118 49 54 desired desire VERB american_scientific_journal-4118 49 55 exact exact ADJ american_scientific_journal-4118 49 56 solution solution NOUN american_scientific_journal-4118 49 57 of of ADP american_scientific_journal-4118 49 58 ( ( PUNCT american_scientific_journal-4118 49 59 3.1 3.1 NUM american_scientific_journal-4118 49 60 ) ) PUNCT american_scientific_journal-4118 49 61 ο£Ύ ο£Ύ NOUN american_scientific_journal-4118 49 62 ο£½ ο£½ PROPN american_scientific_journal-4118 49 63 ο£Ό ο£Ό PROPN american_scientific_journal-4118 49 64 ο£³ ο£³ NOUN american_scientific_journal-4118 49 65 ο£² ο£² ADP american_scientific_journal-4118 49 66 ο£± ο£± PROPN american_scientific_journal-4118 49 67 βˆ’Β± βˆ’Β± NOUN american_scientific_journal-4118 49 68 βˆ’βˆ’ βˆ’βˆ’ NOUN american_scientific_journal-4118 49 69 = = SYM american_scientific_journal-4118 50 1 2 2 NUM american_scientific_journal-4118 50 2 1 1 NUM american_scientific_journal-4118 50 3 22 22 NUM american_scientific_journal-4118 50 4 1 1 NUM american_scientific_journal-4118 50 5 ) ) PUNCT american_scientific_journal-4118 50 6 ] ] PUNCT american_scientific_journal-4118 50 7 ( ( PUNCT american_scientific_journal-4118 50 8 [ [ PUNCT american_scientific_journal-4118 50 9 ) ) PUNCT american_scientific_journal-4118 50 10 ( ( PUNCT american_scientific_journal-4118 50 11 2ln1 2ln1 NUM american_scientific_journal-4118 50 12 ) ) PUNCT american_scientific_journal-4118 50 13 , , PUNCT american_scientific_journal-4118 50 14 ( ( PUNCT american_scientific_journal-4118 50 15 ctxcb ctxcb VERB american_scientific_journal-4118 50 16 catxw catxw PROPN american_scientific_journal-4118 50 17 Ξ²Ξ² Ξ²Ξ² PROPN american_scientific_journal-4118 50 18 ( ( PUNCT american_scientific_journal-4118 50 19 3.8 3.8 NUM american_scientific_journal-4118 50 20 ) ) PUNCT american_scientific_journal-4118 50 21 similarly similarly ADV american_scientific_journal-4118 50 22 , , PUNCT american_scientific_journal-4118 50 23 for for ADP american_scientific_journal-4118 50 24 , , PUNCT american_scientific_journal-4118 50 25 .... .... PROPN american_scientific_journal-4118 50 26 7,6,5,4,3 7,6,5,4,3 NUM american_scientific_journal-4118 51 1 = = SYM american_scientific_journal-4118 51 2 n n NUM american_scientific_journal-4118 51 3 the the DET american_scientific_journal-4118 51 4 corresponding corresponding ADJ american_scientific_journal-4118 51 5 exact exact ADJ american_scientific_journal-4118 51 6 solutions solution NOUN american_scientific_journal-4118 51 7 of of ADP american_scientific_journal-4118 51 8 eq eq PROPN american_scientific_journal-4118 51 9 . . PUNCT american_scientific_journal-4118 52 1 ( ( PUNCT american_scientific_journal-4118 52 2 3.1 3.1 NUM american_scientific_journal-4118 52 3 ) ) PUNCT american_scientific_journal-4118 52 4 are be AUX american_scientific_journal-4118 52 5 ( ( PUNCT american_scientific_journal-4118 52 6 b b NOUN american_scientific_journal-4118 52 7 ) ) PUNCT american_scientific_journal-4118 52 8 3 3 NUM american_scientific_journal-4118 52 9 = = SYM american_scientific_journal-4118 52 10 n n NUM american_scientific_journal-4118 52 11 , , PUNCT american_scientific_journal-4118 52 12 ο£Ύ ο£Ύ NOUN american_scientific_journal-4118 52 13 ο£½ ο£½ PROPN american_scientific_journal-4118 52 14 ο£Ό ο£Ό PROPN american_scientific_journal-4118 52 15 ο£³ ο£³ NOUN american_scientific_journal-4118 52 16 ο£² ο£² ADP american_scientific_journal-4118 52 17 ο£± ο£± PROPN american_scientific_journal-4118 52 18 βˆ’Β± βˆ’Β± NOUN american_scientific_journal-4118 52 19 βˆ’βˆ’ βˆ’βˆ’ NOUN american_scientific_journal-4118 52 20 = = SYM american_scientific_journal-4118 52 21 2 2 NUM american_scientific_journal-4118 52 22 1 1 NUM american_scientific_journal-4118 52 23 22 22 NUM american_scientific_journal-4118 52 24 2 2 NUM american_scientific_journal-4118 52 25 ) ) PUNCT american_scientific_journal-4118 52 26 ] ] PUNCT american_scientific_journal-4118 52 27 ( ( PUNCT american_scientific_journal-4118 52 28 2 2 NUM american_scientific_journal-4118 52 29 [ [ PUNCT american_scientific_journal-4118 52 30 ) ) PUNCT american_scientific_journal-4118 52 31 ( ( PUNCT american_scientific_journal-4118 52 32 8ln1 8ln1 NOUN american_scientific_journal-4118 52 33 ) ) PUNCT american_scientific_journal-4118 52 34 , , PUNCT american_scientific_journal-4118 52 35 ( ( PUNCT american_scientific_journal-4118 52 36 ctxcb ctxcb VERB american_scientific_journal-4118 52 37 catxw catxw PROPN american_scientific_journal-4118 52 38 Ξ²Ξ² Ξ²Ξ² PROPN american_scientific_journal-4118 52 39 ( ( PUNCT american_scientific_journal-4118 52 40 c c NOUN american_scientific_journal-4118 52 41 ) ) PUNCT american_scientific_journal-4118 52 42 4 4 NUM american_scientific_journal-4118 52 43 = = SYM american_scientific_journal-4118 52 44 n n PRON american_scientific_journal-4118 52 45 ο£Ύ ο£Ύ NOUN american_scientific_journal-4118 52 46 ο£½ ο£½ PROPN american_scientific_journal-4118 52 47 ο£Ό ο£Ό PROPN american_scientific_journal-4118 52 48 ο£³ ο£³ NOUN american_scientific_journal-4118 52 49 ο£² ο£² ADP american_scientific_journal-4118 52 50 ο£± ο£± PROPN american_scientific_journal-4118 52 51 βˆ’Β± βˆ’Β± NOUN american_scientific_journal-4118 52 52 βˆ’βˆ’ βˆ’βˆ’ NOUN american_scientific_journal-4118 52 53 = = SYM american_scientific_journal-4118 52 54 2 2 NUM american_scientific_journal-4118 52 55 1 1 NUM american_scientific_journal-4118 52 56 22 22 NUM american_scientific_journal-4118 52 57 3 3 NUM american_scientific_journal-4118 52 58 ) ) PUNCT american_scientific_journal-4118 52 59 ] ] X american_scientific_journal-4118 52 60 ( ( PUNCT american_scientific_journal-4118 52 61 3 3 NUM american_scientific_journal-4118 52 62 [ [ NOUN american_scientific_journal-4118 52 63 ) ) PUNCT american_scientific_journal-4118 52 64 ( ( PUNCT american_scientific_journal-4118 52 65 18ln1 18ln1 NOUN american_scientific_journal-4118 52 66 ) ) PUNCT american_scientific_journal-4118 52 67 , , PUNCT american_scientific_journal-4118 52 68 ( ( PUNCT american_scientific_journal-4118 52 69 ctxcb ctxcb VERB american_scientific_journal-4118 52 70 catxw catxw PROPN american_scientific_journal-4118 52 71 Ξ²Ξ² Ξ²Ξ² PROPN american_scientific_journal-4118 53 1 ( ( PUNCT american_scientific_journal-4118 53 2 d d NOUN american_scientific_journal-4118 53 3 ) ) PUNCT american_scientific_journal-4118 53 4 5 5 NUM american_scientific_journal-4118 53 5 = = SYM american_scientific_journal-4118 53 6 n n PRON american_scientific_journal-4118 53 7 ο£Ύ ο£Ύ NOUN american_scientific_journal-4118 53 8 ο£½ ο£½ PROPN american_scientific_journal-4118 53 9 ο£Ό ο£Ό PROPN american_scientific_journal-4118 53 10 ο£³ ο£³ NOUN american_scientific_journal-4118 53 11 ο£² ο£² ADP american_scientific_journal-4118 53 12 ο£± ο£± PROPN american_scientific_journal-4118 53 13 βˆ’Β± βˆ’Β± NOUN american_scientific_journal-4118 53 14 βˆ’βˆ’ βˆ’βˆ’ NOUN american_scientific_journal-4118 53 15 = = SYM american_scientific_journal-4118 53 16 2 2 NUM american_scientific_journal-4118 53 17 1 1 NUM american_scientific_journal-4118 53 18 22 22 NUM american_scientific_journal-4118 53 19 4 4 NUM american_scientific_journal-4118 53 20 ) ) PUNCT american_scientific_journal-4118 53 21 ] ] X american_scientific_journal-4118 53 22 ( ( PUNCT american_scientific_journal-4118 53 23 4 4 NUM american_scientific_journal-4118 53 24 [ [ NOUN american_scientific_journal-4118 53 25 ) ) PUNCT american_scientific_journal-4118 53 26 ( ( PUNCT american_scientific_journal-4118 53 27 32ln1 32ln1 NOUN american_scientific_journal-4118 53 28 ) ) PUNCT american_scientific_journal-4118 53 29 , , PUNCT american_scientific_journal-4118 53 30 ( ( PUNCT american_scientific_journal-4118 53 31 ctxcb ctxcb VERB american_scientific_journal-4118 53 32 catxw catxw PROPN american_scientific_journal-4118 53 33 Ξ²Ξ² Ξ²Ξ² PROPN american_scientific_journal-4118 53 34 ( ( PUNCT american_scientific_journal-4118 53 35 e e NOUN american_scientific_journal-4118 53 36 ) ) PUNCT american_scientific_journal-4118 53 37 6 6 NUM american_scientific_journal-4118 53 38 = = SYM american_scientific_journal-4118 53 39 n n PRON american_scientific_journal-4118 53 40 ο£Ύ ο£Ύ NOUN american_scientific_journal-4118 53 41 ο£½ ο£½ PROPN american_scientific_journal-4118 53 42 ο£Ό ο£Ό PROPN american_scientific_journal-4118 53 43 ο£³ ο£³ NOUN american_scientific_journal-4118 53 44 ο£² ο£² ADP american_scientific_journal-4118 53 45 ο£± ο£± PROPN american_scientific_journal-4118 53 46 βˆ’Β± βˆ’Β± NOUN american_scientific_journal-4118 53 47 βˆ’βˆ’ βˆ’βˆ’ NOUN american_scientific_journal-4118 53 48 = = SYM american_scientific_journal-4118 53 49 2 2 NUM american_scientific_journal-4118 53 50 1 1 NUM american_scientific_journal-4118 53 51 22 22 NUM american_scientific_journal-4118 53 52 5 5 NUM american_scientific_journal-4118 53 53 ) ) PUNCT american_scientific_journal-4118 53 54 ] ] X american_scientific_journal-4118 53 55 ( ( PUNCT american_scientific_journal-4118 53 56 5 5 NUM american_scientific_journal-4118 53 57 [ [ PUNCT american_scientific_journal-4118 53 58 ) ) PUNCT american_scientific_journal-4118 53 59 ( ( PUNCT american_scientific_journal-4118 53 60 50ln1 50ln1 NOUN american_scientific_journal-4118 53 61 ) ) PUNCT american_scientific_journal-4118 53 62 , , PUNCT american_scientific_journal-4118 53 63 ( ( PUNCT american_scientific_journal-4118 53 64 ctxcb ctxcb VERB american_scientific_journal-4118 53 65 catxw catxw PROPN american_scientific_journal-4118 54 1 Ξ²Ξ² Ξ²Ξ² PROPN american_scientific_journal-4118 55 1 ( ( PUNCT american_scientific_journal-4118 55 2 f f X american_scientific_journal-4118 55 3 ) ) PUNCT american_scientific_journal-4118 55 4 7 7 NUM american_scientific_journal-4118 55 5 = = SYM american_scientific_journal-4118 55 6 n n NUM american_scientific_journal-4118 55 7 : : PUNCT american_scientific_journal-4118 55 8 ο£Ύ ο£Ύ PROPN american_scientific_journal-4118 55 9 ο£½ ο£½ PROPN american_scientific_journal-4118 55 10 ο£Ό ο£Ό PROPN american_scientific_journal-4118 55 11 ο£³ ο£³ NOUN american_scientific_journal-4118 55 12 ο£² ο£² ADP american_scientific_journal-4118 55 13 ο£± ο£± PROPN american_scientific_journal-4118 55 14 βˆ’Β± βˆ’Β± NOUN american_scientific_journal-4118 55 15 βˆ’βˆ’ βˆ’βˆ’ NOUN american_scientific_journal-4118 55 16 = = SYM american_scientific_journal-4118 55 17 2 2 NUM american_scientific_journal-4118 55 18 1 1 NUM american_scientific_journal-4118 55 19 22 22 NUM american_scientific_journal-4118 55 20 6 6 NUM american_scientific_journal-4118 55 21 ) ) PUNCT american_scientific_journal-4118 55 22 ] ] X american_scientific_journal-4118 55 23 ( ( PUNCT american_scientific_journal-4118 55 24 6 6 NUM american_scientific_journal-4118 55 25 [ [ PUNCT american_scientific_journal-4118 55 26 ) ) PUNCT american_scientific_journal-4118 55 27 ( ( PUNCT american_scientific_journal-4118 55 28 72ln1 72ln1 NOUN american_scientific_journal-4118 55 29 ) ) PUNCT american_scientific_journal-4118 55 30 , , PUNCT american_scientific_journal-4118 55 31 ( ( PUNCT american_scientific_journal-4118 55 32 ctxcb ctxcb VERB american_scientific_journal-4118 55 33 catxw catxw NOUN american_scientific_journal-4118 55 34 Ξ²Ξ² Ξ²Ξ² PROPN american_scientific_journal-4118 55 35 in in ADP american_scientific_journal-4118 55 36 general general ADJ american_scientific_journal-4118 55 37 , , PUNCT american_scientific_journal-4118 55 38 the the DET american_scientific_journal-4118 55 39 solution solution NOUN american_scientific_journal-4118 55 40 of of ADP american_scientific_journal-4118 55 41 ( ( PUNCT american_scientific_journal-4118 55 42 3.1 3.1 NUM american_scientific_journal-4118 55 43 ) ) PUNCT american_scientific_journal-4118 55 44 is be AUX american_scientific_journal-4118 55 45 ο£Ύ ο£Ύ NOUN american_scientific_journal-4118 55 46 ο£½ ο£½ PROPN american_scientific_journal-4118 55 47 ο£Ό ο£Ό PROPN american_scientific_journal-4118 55 48 ο£³ ο£³ NOUN american_scientific_journal-4118 55 49 ο£² ο£² ADP american_scientific_journal-4118 55 50 ο£± ο£± PROPN american_scientific_journal-4118 55 51 βˆ’βˆ’Β± βˆ’βˆ’Β± NOUN american_scientific_journal-4118 55 52 βˆ’βˆ’βˆ’ βˆ’βˆ’βˆ’ PUNCT american_scientific_journal-4118 56 1 = = NOUN american_scientific_journal-4118 56 2 βˆ’ βˆ’ PROPN american_scientific_journal-4118 56 3 2 2 NUM american_scientific_journal-4118 56 4 1 1 NUM american_scientific_journal-4118 56 5 222 222 NUM american_scientific_journal-4118 56 6 1 1 NUM american_scientific_journal-4118 56 7 ) ) PUNCT american_scientific_journal-4118 56 8 ] ] PUNCT american_scientific_journal-4118 56 9 ) ) PUNCT american_scientific_journal-4118 56 10 ( ( PUNCT american_scientific_journal-4118 56 11 1 1 NUM american_scientific_journal-4118 56 12 ( ( PUNCT american_scientific_journal-4118 56 13 [ [ PUNCT american_scientific_journal-4118 56 14 ) ) PUNCT american_scientific_journal-4118 56 15 ( ( PUNCT american_scientific_journal-4118 56 16 ) ) PUNCT american_scientific_journal-4118 56 17 1(2ln1 1(2ln1 NOUN american_scientific_journal-4118 56 18 ) ) PUNCT american_scientific_journal-4118 56 19 ( ( PUNCT american_scientific_journal-4118 56 20 ctxncb ctxncb PROPN american_scientific_journal-4118 56 21 canwn canwn VERB american_scientific_journal-4118 56 22 Ξ²Ξ² Ξ²Ξ² PROPN american_scientific_journal-4118 56 23 ΞΎ ΞΎ PROPN american_scientific_journal-4118 56 24 , , PUNCT american_scientific_journal-4118 56 25 where where SCONJ american_scientific_journal-4118 56 26 0 0 NUM american_scientific_journal-4118 56 27 ) ) PUNCT american_scientific_journal-4118 56 28 ] ] X american_scientific_journal-4118 56 29 ) ) PUNCT american_scientific_journal-4118 56 30 ( ( PUNCT american_scientific_journal-4118 56 31 1 1 NUM american_scientific_journal-4118 56 32 ( ( PUNCT american_scientific_journal-4118 56 33 [ [ PUNCT american_scientific_journal-4118 56 34 ) ) PUNCT american_scientific_journal-4118 56 35 ( ( PUNCT american_scientific_journal-4118 56 36 ) ) PUNCT american_scientific_journal-4118 56 37 1(2 1(2 PROPN american_scientific_journal-4118 57 1 2 2 NUM american_scientific_journal-4118 57 2 1 1 NUM american_scientific_journal-4118 57 3 222 222 NUM american_scientific_journal-4118 57 4 > > X american_scientific_journal-4118 57 5 βˆ’βˆ’Β± βˆ’βˆ’Β± NOUN american_scientific_journal-4118 57 6 βˆ’βˆ’βˆ’ βˆ’βˆ’βˆ’ X american_scientific_journal-4118 57 7 ctxncb ctxncb PROPN american_scientific_journal-4118 57 8 can can AUX american_scientific_journal-4118 57 9 Ξ² Ξ² X american_scientific_journal-4118 57 10 ( ( PUNCT american_scientific_journal-4118 57 11 3.9 3.9 NUM american_scientific_journal-4118 57 12 ) ) PUNCT american_scientific_journal-4118 57 13 singularity singularity NOUN american_scientific_journal-4118 57 14 : : PUNCT american_scientific_journal-4118 57 15 from from ADP american_scientific_journal-4118 57 16 the the DET american_scientific_journal-4118 57 17 above above ADJ american_scientific_journal-4118 57 18 obtained obtain VERB american_scientific_journal-4118 57 19 solutions solution NOUN american_scientific_journal-4118 57 20 we we PRON american_scientific_journal-4118 57 21 observe observe VERB american_scientific_journal-4118 57 22 that that SCONJ american_scientific_journal-4118 57 23 the the DET american_scientific_journal-4118 57 24 solutions solution NOUN american_scientific_journal-4118 57 25 have have VERB american_scientific_journal-4118 57 26 singularities singularity NOUN american_scientific_journal-4118 57 27 for for ADP american_scientific_journal-4118 57 28 the the DET american_scientific_journal-4118 57 29 values value NOUN american_scientific_journal-4118 57 30 x x PUNCT american_scientific_journal-4118 57 31 and and CCONJ american_scientific_journal-4118 57 32 t t X american_scientific_journal-4118 57 33 satisfying satisfy VERB american_scientific_journal-4118 57 34 2,0))(1(1 2,0))(1(1 NOUN american_scientific_journal-4118 57 35 β‰₯=βˆ’βˆ’Β± β‰₯=βˆ’βˆ’Β± PROPN american_scientific_journal-4118 57 36 nctxnc nctxnc PROPN american_scientific_journal-4118 57 37 or or CCONJ american_scientific_journal-4118 57 38 .0 .0 NUM american_scientific_journal-4118 57 39 ) ) PUNCT american_scientific_journal-4118 57 40 ] ] PUNCT american_scientific_journal-4118 57 41 ) ) PUNCT american_scientific_journal-4118 57 42 ( ( PUNCT american_scientific_journal-4118 57 43 1 1 NUM american_scientific_journal-4118 57 44 ( ( PUNCT american_scientific_journal-4118 57 45 [ [ PUNCT american_scientific_journal-4118 57 46 ) ) PUNCT american_scientific_journal-4118 57 47 ( ( PUNCT american_scientific_journal-4118 57 48 ) ) PUNCT american_scientific_journal-4118 57 49 1(2 1(2 PROPN american_scientific_journal-4118 57 50 2 2 NUM american_scientific_journal-4118 57 51 1 1 NUM american_scientific_journal-4118 57 52 222 222 NUM american_scientific_journal-4118 57 53 > > X american_scientific_journal-4118 57 54 βˆ’βˆ’Β± βˆ’βˆ’Β± PROPN american_scientific_journal-4118 57 55 βˆ’βˆ’ βˆ’βˆ’ PROPN american_scientific_journal-4118 57 56 ctxncb ctxncb NOUN american_scientific_journal-4118 57 57 can can AUX american_scientific_journal-4118 57 58 Ξ² Ξ² NOUN american_scientific_journal-4118 57 59 justification justification NOUN american_scientific_journal-4118 57 60 : : PUNCT american_scientific_journal-4118 57 61 here here ADV american_scientific_journal-4118 57 62 , , PUNCT american_scientific_journal-4118 57 63 𝑀𝑀𝑖𝑖(π‘₯π‘₯ 𝑀𝑀𝑖𝑖(π‘₯π‘₯ NOUN american_scientific_journal-4118 57 64 , , PUNCT american_scientific_journal-4118 57 65 𝑑𝑑 𝑑𝑑 PROPN american_scientific_journal-4118 57 66 ) ) PUNCT american_scientific_journal-4118 57 67 , , PUNCT american_scientific_journal-4118 57 68 𝑖𝑖 𝑖𝑖 X american_scientific_journal-4118 57 69 = = SYM american_scientific_journal-4118 58 1 1,2,3,4,5,6 1,2,3,4,5,6 NUM american_scientific_journal-4118 58 2 obtained obtain VERB american_scientific_journal-4118 58 3 in in ADP american_scientific_journal-4118 58 4 different different ADJ american_scientific_journal-4118 58 5 cases case NOUN american_scientific_journal-4118 58 6 are be AUX american_scientific_journal-4118 58 7 exact exact ADJ american_scientific_journal-4118 58 8 solutions solution NOUN american_scientific_journal-4118 58 9 of of ADP american_scientific_journal-4118 58 10 the the DET american_scientific_journal-4118 58 11 modified modify VERB american_scientific_journal-4118 58 12 liouville liouville NOUN american_scientific_journal-4118 58 13 equation equation NOUN american_scientific_journal-4118 58 14 because because SCONJ american_scientific_journal-4118 58 15 they they PRON american_scientific_journal-4118 58 16 fully fully ADV american_scientific_journal-4118 58 17 satisfy satisfy VERB american_scientific_journal-4118 58 18 the the DET american_scientific_journal-4118 58 19 equation equation NOUN american_scientific_journal-4118 58 20 ( ( PUNCT american_scientific_journal-4118 58 21 3.1 3.1 NUM american_scientific_journal-4118 58 22 ) ) PUNCT american_scientific_journal-4118 58 23 . . PUNCT american_scientific_journal-4118 59 1 this this DET american_scientific_journal-4118 59 2 justification justification NOUN american_scientific_journal-4118 59 3 is be AUX american_scientific_journal-4118 59 4 checked check VERB american_scientific_journal-4118 59 5 by by ADP american_scientific_journal-4118 59 6 maple-13 maple-13 PROPN american_scientific_journal-4118 59 7 and and CCONJ american_scientific_journal-4118 59 8 the the DET american_scientific_journal-4118 59 9 corresponding correspond VERB american_scientific_journal-4118 59 10 maple maple NOUN american_scientific_journal-4118 59 11 code code NOUN american_scientific_journal-4118 59 12 is be AUX american_scientific_journal-4118 59 13 given give VERB american_scientific_journal-4118 59 14 below below ADV american_scientific_journal-4118 59 15 : : PUNCT american_scientific_journal-4118 59 16 american american ADJ american_scientific_journal-4118 59 17 scientific scientific ADJ american_scientific_journal-4118 59 18 research research PROPN american_scientific_journal-4118 59 19 journal journal NOUN american_scientific_journal-4118 59 20 for for ADP american_scientific_journal-4118 59 21 engineering engineering NOUN american_scientific_journal-4118 59 22 , , PUNCT american_scientific_journal-4118 59 23 technology technology NOUN american_scientific_journal-4118 59 24 , , PUNCT american_scientific_journal-4118 59 25 and and CCONJ american_scientific_journal-4118 59 26 sciences science NOUN american_scientific_journal-4118 59 27 ( ( PUNCT american_scientific_journal-4118 59 28 asrjets asrjet NOUN american_scientific_journal-4118 59 29 ) ) PUNCT american_scientific_journal-4118 59 30 ( ( PUNCT american_scientific_journal-4118 59 31 2018 2018 NUM american_scientific_journal-4118 59 32 ) ) PUNCT american_scientific_journal-4118 59 33 volume volume NOUN american_scientific_journal-4118 59 34 44 44 NUM american_scientific_journal-4118 59 35 , , PUNCT american_scientific_journal-4118 59 36 no no DET american_scientific_journal-4118 59 37 1 1 NUM american_scientific_journal-4118 59 38 , , PUNCT american_scientific_journal-4118 59 39 pp pp ADV american_scientific_journal-4118 59 40 58 58 NUM american_scientific_journal-4118 59 41 - - SYM american_scientific_journal-4118 59 42 67 67 NUM american_scientific_journal-4118 59 43 63 63 NUM american_scientific_journal-4118 59 44 * * PUNCT american_scientific_journal-4118 59 45 justification justification NOUN american_scientific_journal-4118 59 46 of of ADP american_scientific_journal-4118 59 47 the the DET american_scientific_journal-4118 59 48 solutions solution NOUN american_scientific_journal-4118 59 49 of of ADP american_scientific_journal-4118 59 50 the the DET american_scientific_journal-4118 59 51 modified modify VERB american_scientific_journal-4118 59 52 liouville liouville NOUN american_scientific_journal-4118 59 53 equation equation NOUN american_scientific_journal-4118 59 54 * * PUNCT american_scientific_journal-4118 59 55 > > X american_scientific_journal-4118 59 56 > > X american_scientific_journal-4118 59 57 > > X american_scientific_journal-4118 59 58 ο£Ύ ο£Ύ PROPN american_scientific_journal-4118 59 59 ο£½ ο£½ PROPN american_scientific_journal-4118 59 60 ο£Ό ο£Ό PROPN american_scientific_journal-4118 59 61 ο£³ ο£³ NOUN american_scientific_journal-4118 59 62 ο£² ο£² ADP american_scientific_journal-4118 59 63 ο£± ο£± PROPN american_scientific_journal-4118 59 64 βˆ’βˆ’Β± βˆ’βˆ’Β± NOUN american_scientific_journal-4118 59 65 βˆ’βˆ’βˆ’ βˆ’βˆ’βˆ’ PUNCT american_scientific_journal-4118 60 1 = = NOUN american_scientific_journal-4118 60 2 βˆ’ βˆ’ PROPN american_scientific_journal-4118 60 3 2 2 NUM american_scientific_journal-4118 60 4 1 1 NUM american_scientific_journal-4118 60 5 222 222 NUM american_scientific_journal-4118 60 6 1 1 NUM american_scientific_journal-4118 60 7 ) ) PUNCT american_scientific_journal-4118 60 8 ] ] PUNCT american_scientific_journal-4118 60 9 ) ) PUNCT american_scientific_journal-4118 60 10 ( ( PUNCT american_scientific_journal-4118 60 11 1 1 NUM american_scientific_journal-4118 60 12 ( ( PUNCT american_scientific_journal-4118 60 13 [ [ PUNCT american_scientific_journal-4118 60 14 ) ) PUNCT american_scientific_journal-4118 60 15 ( ( PUNCT american_scientific_journal-4118 60 16 ) ) PUNCT american_scientific_journal-4118 60 17 1(2ln1 1(2ln1 NOUN american_scientific_journal-4118 60 18 ) ) PUNCT american_scientific_journal-4118 60 19 ( ( PUNCT american_scientific_journal-4118 60 20 ctxncb ctxncb PROPN american_scientific_journal-4118 60 21 canwn canwn VERB american_scientific_journal-4118 60 22 Ξ²Ξ² Ξ²Ξ² PROPN american_scientific_journal-4118 61 1 ΞΎ ΞΎ X american_scientific_journal-4118 61 2 > > SYM american_scientific_journal-4118 61 3 0 0 NUM american_scientific_journal-4118 61 4 figure figure NOUN american_scientific_journal-4118 61 5 3 3 NUM american_scientific_journal-4118 61 6 velocity velocity NOUN american_scientific_journal-4118 61 7 profile profile NOUN american_scientific_journal-4118 61 8 of of ADP american_scientific_journal-4118 61 9 𝑀𝑀1(π‘₯π‘₯ 𝑀𝑀1(π‘₯π‘₯ PROPN american_scientific_journal-4118 61 10 , , PUNCT american_scientific_journal-4118 61 11 𝑑𝑑 𝑑𝑑 PROPN american_scientific_journal-4118 61 12 ) ) PUNCT american_scientific_journal-4118 61 13 with with ADP american_scientific_journal-4118 61 14 wave wave NOUN american_scientific_journal-4118 61 15 speed speed NOUN american_scientific_journal-4118 61 16 , , PUNCT american_scientific_journal-4118 61 17 c=2 c=2 PRON american_scientific_journal-4118 61 18 figure figure VERB american_scientific_journal-4118 61 19 3.1 3.1 NUM american_scientific_journal-4118 61 20 : : PUNCT american_scientific_journal-4118 61 21 ( ( PUNCT american_scientific_journal-4118 61 22 3d 3d NUM american_scientific_journal-4118 61 23 plot plot NOUN american_scientific_journal-4118 61 24 ): ): PUNCT american_scientific_journal-4118 61 25 profile profile NOUN american_scientific_journal-4118 61 26 of of ADP american_scientific_journal-4118 61 27 ( ( PUNCT american_scientific_journal-4118 61 28 3.9 3.9 NUM american_scientific_journal-4118 61 29 ) ) PUNCT american_scientific_journal-4118 61 30 , , PUNCT american_scientific_journal-4118 61 31 when when SCONJ american_scientific_journal-4118 61 32 𝑙𝑙 𝑙𝑙 PROPN american_scientific_journal-4118 61 33 = = SYM american_scientific_journal-4118 61 34 2 2 NUM american_scientific_journal-4118 61 35 , , PUNCT american_scientific_journal-4118 61 36 π‘Žπ‘Ž π‘Žπ‘Ž NOUN american_scientific_journal-4118 61 37 = = SYM american_scientific_journal-4118 61 38 1 1 NUM american_scientific_journal-4118 61 39 , , PUNCT american_scientific_journal-4118 61 40 𝑐𝑐1 𝑐𝑐1 PROPN american_scientific_journal-4118 61 41 = = SYM american_scientific_journal-4118 61 42 1 1 NUM american_scientific_journal-4118 61 43 , , PUNCT american_scientific_journal-4118 61 44 𝑏𝑏 𝑏𝑏 NOUN american_scientific_journal-4118 61 45 = = SYM american_scientific_journal-4118 61 46 1,𝛽𝛽 1,𝛽𝛽 NUM american_scientific_journal-4118 61 47 = = SYM american_scientific_journal-4118 61 48 1 1 NUM american_scientific_journal-4118 61 49 figure figure NOUN american_scientific_journal-4118 61 50 3.2 3.2 NUM american_scientific_journal-4118 61 51 : : PUNCT american_scientific_journal-4118 61 52 ( ( PUNCT american_scientific_journal-4118 61 53 2d 2d NUM american_scientific_journal-4118 61 54 plot plot NOUN american_scientific_journal-4118 61 55 ): ): PUNCT american_scientific_journal-4118 61 56 profile profile NOUN american_scientific_journal-4118 61 57 of of ADP american_scientific_journal-4118 61 58 ( ( PUNCT american_scientific_journal-4118 61 59 3.9 3.9 NUM american_scientific_journal-4118 61 60 ) ) PUNCT american_scientific_journal-4118 61 61 , , PUNCT american_scientific_journal-4118 61 62 when when SCONJ american_scientific_journal-4118 61 63 𝑙𝑙 𝑙𝑙 PROPN american_scientific_journal-4118 61 64 = = SYM american_scientific_journal-4118 61 65 2 2 NUM american_scientific_journal-4118 61 66 , , PUNCT american_scientific_journal-4118 61 67 π‘Žπ‘Ž π‘Žπ‘Ž NOUN american_scientific_journal-4118 61 68 = = SYM american_scientific_journal-4118 61 69 1 1 NUM american_scientific_journal-4118 61 70 , , PUNCT american_scientific_journal-4118 61 71 𝑐𝑐1 𝑐𝑐1 PROPN american_scientific_journal-4118 61 72 = = SYM american_scientific_journal-4118 62 1 1 1 NUM american_scientific_journal-4118 62 2 , , PUNCT american_scientific_journal-4118 62 3 𝑏𝑏 𝑏𝑏 NOUN american_scientific_journal-4118 62 4 = = SYM american_scientific_journal-4118 62 5 1,𝛽𝛽 1,𝛽𝛽 NUM american_scientific_journal-4118 62 6 = = SYM american_scientific_journal-4118 62 7 1 1 NUM american_scientific_journal-4118 62 8 and and CCONJ american_scientific_journal-4118 62 9 time time NOUN american_scientific_journal-4118 62 10 t=1 t=1 PROPN american_scientific_journal-4118 62 11 . . PUNCT american_scientific_journal-4118 63 1 velocity velocity NOUN american_scientific_journal-4118 63 2 profile profile NOUN american_scientific_journal-4118 63 3 of of ADP american_scientific_journal-4118 63 4 𝑀𝑀1(π‘₯π‘₯ 𝑀𝑀1(π‘₯π‘₯ PROPN american_scientific_journal-4118 63 5 , , PUNCT american_scientific_journal-4118 63 6 𝑑𝑑 𝑑𝑑 PROPN american_scientific_journal-4118 63 7 ) ) PUNCT american_scientific_journal-4118 63 8 with with ADP american_scientific_journal-4118 63 9 wave wave NOUN american_scientific_journal-4118 63 10 speed speed NOUN american_scientific_journal-4118 63 11 , , PUNCT american_scientific_journal-4118 63 12 c=3 c=3 PROPN american_scientific_journal-4118 63 13 american american ADJ american_scientific_journal-4118 63 14 scientific scientific ADJ american_scientific_journal-4118 63 15 research research NOUN american_scientific_journal-4118 63 16 journal journal NOUN american_scientific_journal-4118 63 17 for for ADP american_scientific_journal-4118 63 18 engineering engineering NOUN american_scientific_journal-4118 63 19 , , PUNCT american_scientific_journal-4118 63 20 technology technology NOUN american_scientific_journal-4118 63 21 , , PUNCT american_scientific_journal-4118 63 22 and and CCONJ american_scientific_journal-4118 63 23 sciences science NOUN american_scientific_journal-4118 63 24 ( ( PUNCT american_scientific_journal-4118 63 25 asrjets asrjet NOUN american_scientific_journal-4118 63 26 ) ) PUNCT american_scientific_journal-4118 63 27 ( ( PUNCT american_scientific_journal-4118 63 28 2018 2018 NUM american_scientific_journal-4118 63 29 ) ) PUNCT american_scientific_journal-4118 63 30 volume volume NOUN american_scientific_journal-4118 63 31 44 44 NUM american_scientific_journal-4118 63 32 , , PUNCT american_scientific_journal-4118 63 33 no no DET american_scientific_journal-4118 63 34 1 1 NUM american_scientific_journal-4118 63 35 , , PUNCT american_scientific_journal-4118 63 36 pp pp ADV american_scientific_journal-4118 63 37 58 58 NUM american_scientific_journal-4118 63 38 - - SYM american_scientific_journal-4118 63 39 67 67 NUM american_scientific_journal-4118 63 40 64 64 NUM american_scientific_journal-4118 63 41 figure figure NOUN american_scientific_journal-4118 63 42 3.3 3.3 NUM american_scientific_journal-4118 63 43 : : PUNCT american_scientific_journal-4118 63 44 ( ( PUNCT american_scientific_journal-4118 63 45 3d 3d NUM american_scientific_journal-4118 63 46 plot plot NOUN american_scientific_journal-4118 63 47 ): ): PUNCT american_scientific_journal-4118 63 48 profile profile NOUN american_scientific_journal-4118 63 49 of of ADP american_scientific_journal-4118 63 50 ( ( PUNCT american_scientific_journal-4118 63 51 3.9 3.9 NUM american_scientific_journal-4118 63 52 ) ) PUNCT american_scientific_journal-4118 63 53 , , PUNCT american_scientific_journal-4118 63 54 when when SCONJ american_scientific_journal-4118 63 55 𝑙𝑙 𝑙𝑙 PROPN american_scientific_journal-4118 63 56 = = SYM american_scientific_journal-4118 63 57 2 2 NUM american_scientific_journal-4118 63 58 , , PUNCT american_scientific_journal-4118 63 59 π‘Žπ‘Ž π‘Žπ‘Ž NOUN american_scientific_journal-4118 63 60 = = SYM american_scientific_journal-4118 63 61 1 1 NUM american_scientific_journal-4118 63 62 , , PUNCT american_scientific_journal-4118 63 63 𝑐𝑐1 𝑐𝑐1 PROPN american_scientific_journal-4118 63 64 = = SYM american_scientific_journal-4118 64 1 1 1 NUM american_scientific_journal-4118 64 2 , , PUNCT american_scientific_journal-4118 64 3 𝑏𝑏 𝑏𝑏 NOUN american_scientific_journal-4118 64 4 = = SYM american_scientific_journal-4118 64 5 1,𝛽𝛽 1,𝛽𝛽 NUM american_scientific_journal-4118 64 6 = = SYM american_scientific_journal-4118 64 7 1 1 NUM american_scientific_journal-4118 64 8 figure figure NOUN american_scientific_journal-4118 64 9 3.4 3.4 NUM american_scientific_journal-4118 64 10 : : PUNCT american_scientific_journal-4118 64 11 ( ( PUNCT american_scientific_journal-4118 64 12 2d 2d NUM american_scientific_journal-4118 64 13 plot plot NOUN american_scientific_journal-4118 64 14 ): ): PUNCT american_scientific_journal-4118 64 15 profile profile NOUN american_scientific_journal-4118 64 16 of of ADP american_scientific_journal-4118 64 17 ( ( PUNCT american_scientific_journal-4118 64 18 3.9 3.9 NUM american_scientific_journal-4118 64 19 ) ) PUNCT american_scientific_journal-4118 64 20 , , PUNCT american_scientific_journal-4118 64 21 when when SCONJ american_scientific_journal-4118 64 22 𝑙𝑙 𝑙𝑙 PROPN american_scientific_journal-4118 64 23 = = SYM american_scientific_journal-4118 64 24 2 2 NUM american_scientific_journal-4118 64 25 , , PUNCT american_scientific_journal-4118 64 26 π‘Žπ‘Ž π‘Žπ‘Ž NOUN american_scientific_journal-4118 64 27 = = SYM american_scientific_journal-4118 64 28 1 1 NUM american_scientific_journal-4118 64 29 , , PUNCT american_scientific_journal-4118 64 30 𝑐𝑐1 𝑐𝑐1 PROPN american_scientific_journal-4118 64 31 = = SYM american_scientific_journal-4118 64 32 1 1 NUM american_scientific_journal-4118 64 33 , , PUNCT american_scientific_journal-4118 64 34 𝑏𝑏 𝑏𝑏 NOUN american_scientific_journal-4118 64 35 = = SYM american_scientific_journal-4118 64 36 1,𝛽𝛽 1,𝛽𝛽 NUM american_scientific_journal-4118 64 37 = = SYM american_scientific_journal-4118 64 38 1 1 NUM american_scientific_journal-4118 64 39 and and CCONJ american_scientific_journal-4118 64 40 time time NOUN american_scientific_journal-4118 64 41 t=1 t=1 PRON american_scientific_journal-4118 64 42 . . PUNCT american_scientific_journal-4118 65 1 example-2 example-2 NUM american_scientific_journal-4118 65 2 : : PUNCT american_scientific_journal-4118 65 3 solution solution NOUN american_scientific_journal-4118 65 4 of of ADP american_scientific_journal-4118 65 5 regularized regularize VERB american_scientific_journal-4118 65 6 long long ADJ american_scientific_journal-4118 65 7 - - PUNCT american_scientific_journal-4118 65 8 wave wave NOUN american_scientific_journal-4118 65 9 equation equation NOUN american_scientific_journal-4118 65 10 the the DET american_scientific_journal-4118 65 11 regularized regularize VERB american_scientific_journal-4118 65 12 long long ADJ american_scientific_journal-4118 65 13 - - PUNCT american_scientific_journal-4118 65 14 wave wave NOUN american_scientific_journal-4118 65 15 equation equation NOUN american_scientific_journal-4118 65 16 is be AUX american_scientific_journal-4118 65 17 0,,06 0,,06 NUM american_scientific_journal-4118 65 18 > > PUNCT american_scientific_journal-4118 65 19 = = SYM american_scientific_journal-4118 65 20 βˆ’βˆ’+ βˆ’βˆ’+ PROPN american_scientific_journal-4118 65 21 babuuuauu babuuuauu PROPN american_scientific_journal-4118 65 22 xxtxxt xxtxxt NOUN american_scientific_journal-4118 65 23 ( ( PUNCT american_scientific_journal-4118 65 24 3.10 3.10 NUM american_scientific_journal-4118 65 25 ) ) PUNCT american_scientific_journal-4118 65 26 where where SCONJ american_scientific_journal-4118 65 27 a a DET american_scientific_journal-4118 65 28 , , PUNCT american_scientific_journal-4118 65 29 b b NOUN american_scientific_journal-4118 65 30 are be AUX american_scientific_journal-4118 65 31 real real ADJ american_scientific_journal-4118 65 32 constants[25 constants[25 NOUN american_scientific_journal-4118 65 33 ] ] X american_scientific_journal-4118 65 34 . . PUNCT american_scientific_journal-4118 66 1 in in ADP american_scientific_journal-4118 66 2 the the DET american_scientific_journal-4118 66 3 above above ADJ american_scientific_journal-4118 66 4 procedure procedure NOUN american_scientific_journal-4118 66 5 , , PUNCT american_scientific_journal-4118 66 6 we we PRON american_scientific_journal-4118 66 7 can can AUX american_scientific_journal-4118 66 8 also also ADV american_scientific_journal-4118 66 9 find find VERB american_scientific_journal-4118 66 10 the the DET american_scientific_journal-4118 66 11 solutions solution NOUN american_scientific_journal-4118 66 12 of of ADP american_scientific_journal-4118 66 13 this this DET american_scientific_journal-4118 66 14 equation equation NOUN american_scientific_journal-4118 66 15 and and CCONJ american_scientific_journal-4118 66 16 the the DET american_scientific_journal-4118 66 17 general general ADJ american_scientific_journal-4118 66 18 form form NOUN american_scientific_journal-4118 66 19 of of ADP american_scientific_journal-4118 66 20 the the DET american_scientific_journal-4118 66 21 solution solution NOUN american_scientific_journal-4118 66 22 of of ADP american_scientific_journal-4118 66 23 ( ( PUNCT american_scientific_journal-4118 66 24 3.10 3.10 NUM american_scientific_journal-4118 66 25 ) ) PUNCT american_scientific_journal-4118 66 26 is be AUX american_scientific_journal-4118 66 27 : : PUNCT american_scientific_journal-4118 66 28 0))(1 0))(1 NUM american_scientific_journal-4118 66 29 ( ( PUNCT american_scientific_journal-4118 66 30 , , PUNCT american_scientific_journal-4118 66 31 ) ) PUNCT american_scientific_journal-4118 66 32 ] ] X american_scientific_journal-4118 66 33 ) ) PUNCT american_scientific_journal-4118 67 1 ( ( PUNCT american_scientific_journal-4118 67 2 1 1 NUM american_scientific_journal-4118 67 3 ( ( PUNCT american_scientific_journal-4118 67 4 [ [ PUNCT american_scientific_journal-4118 67 5 ) ) PUNCT american_scientific_journal-4118 67 6 1(2 1(2 PROPN american_scientific_journal-4118 67 7 6 6 NUM american_scientific_journal-4118 67 8 ) ) PUNCT american_scientific_journal-4118 67 9 , , PUNCT american_scientific_journal-4118 67 10 ( ( PUNCT american_scientific_journal-4118 67 11 12 12 NUM american_scientific_journal-4118 67 12 1 1 NUM american_scientific_journal-4118 67 13 2 2 NUM american_scientific_journal-4118 67 14 1 1 NUM american_scientific_journal-4118 67 15 β‰ βˆ’βˆ’Β± β‰ βˆ’βˆ’Β± NOUN american_scientific_journal-4118 67 16 βˆ’βˆ’Β± βˆ’βˆ’Β± NOUN american_scientific_journal-4118 67 17 βˆ’ βˆ’ PROPN american_scientific_journal-4118 68 1 + + CCONJ american_scientific_journal-4118 69 1 βˆ’ βˆ’ PROPN american_scientific_journal-4118 69 2 = = SYM american_scientific_journal-4118 69 3 βˆ’ βˆ’ PROPN american_scientific_journal-4118 69 4 ctxnc ctxnc ADJ american_scientific_journal-4118 69 5 ctxnc ctxnc ADJ american_scientific_journal-4118 69 6 bcncatxun bcncatxun NOUN american_scientific_journal-4118 69 7 ( ( PUNCT american_scientific_journal-4118 69 8 3.11 3.11 NUM american_scientific_journal-4118 69 9 ) ) PUNCT american_scientific_journal-4118 69 10 velocity velocity NOUN american_scientific_journal-4118 69 11 profile profile NOUN american_scientific_journal-4118 69 12 of of ADP american_scientific_journal-4118 69 13 𝑒𝑒1(π‘₯π‘₯ 𝑒𝑒1(π‘₯π‘₯ PROPN american_scientific_journal-4118 69 14 , , PUNCT american_scientific_journal-4118 69 15 𝑑𝑑 𝑑𝑑 PROPN american_scientific_journal-4118 69 16 ) ) PUNCT american_scientific_journal-4118 69 17 with with ADP american_scientific_journal-4118 69 18 wave wave NOUN american_scientific_journal-4118 69 19 speed speed NOUN american_scientific_journal-4118 69 20 , , PUNCT american_scientific_journal-4118 69 21 c=2 c=2 PRON american_scientific_journal-4118 69 22 figure figure VERB american_scientific_journal-4118 69 23 3.5 3.5 NUM american_scientific_journal-4118 69 24 : : PUNCT american_scientific_journal-4118 69 25 ( ( PUNCT american_scientific_journal-4118 69 26 3d 3d NUM american_scientific_journal-4118 69 27 plot plot NOUN american_scientific_journal-4118 69 28 ): ): PUNCT american_scientific_journal-4118 69 29 soliton soliton NOUN american_scientific_journal-4118 69 30 profile profile NOUN american_scientific_journal-4118 69 31 of of ADP american_scientific_journal-4118 69 32 ( ( PUNCT american_scientific_journal-4118 69 33 3.11 3.11 NUM american_scientific_journal-4118 69 34 ) ) PUNCT american_scientific_journal-4118 69 35 , , PUNCT american_scientific_journal-4118 69 36 when when SCONJ american_scientific_journal-4118 69 37 𝑙𝑙 𝑙𝑙 PROPN american_scientific_journal-4118 69 38 = = SYM american_scientific_journal-4118 69 39 2 2 NUM american_scientific_journal-4118 69 40 , , PUNCT american_scientific_journal-4118 69 41 π‘Žπ‘Ž π‘Žπ‘Ž NOUN american_scientific_journal-4118 69 42 = = SYM american_scientific_journal-4118 69 43 1 1 NUM american_scientific_journal-4118 69 44 , , PUNCT american_scientific_journal-4118 69 45 𝑏𝑏 𝑏𝑏 NOUN american_scientific_journal-4118 69 46 = = SYM american_scientific_journal-4118 69 47 1 1 NUM american_scientific_journal-4118 69 48 , , PUNCT american_scientific_journal-4118 69 49 𝑐𝑐1 𝑐𝑐1 PROPN american_scientific_journal-4118 69 50 = = SYM american_scientific_journal-4118 69 51 1 1 NUM american_scientific_journal-4118 69 52 velocity velocity NOUN american_scientific_journal-4118 69 53 profile profile NOUN american_scientific_journal-4118 69 54 of of ADP american_scientific_journal-4118 69 55 𝑒𝑒1(π‘₯π‘₯ 𝑒𝑒1(π‘₯π‘₯ PROPN american_scientific_journal-4118 69 56 , , PUNCT american_scientific_journal-4118 69 57 𝑑𝑑 𝑑𝑑 PROPN american_scientific_journal-4118 69 58 ) ) PUNCT american_scientific_journal-4118 69 59 with with ADP american_scientific_journal-4118 69 60 wave wave NOUN american_scientific_journal-4118 69 61 speed speed NOUN american_scientific_journal-4118 69 62 , , PUNCT american_scientific_journal-4118 69 63 c=3 c=3 PROPN american_scientific_journal-4118 69 64 figure figure NOUN american_scientific_journal-4118 69 65 3.6 3.6 NUM american_scientific_journal-4118 69 66 : : PUNCT american_scientific_journal-4118 69 67 ( ( PUNCT american_scientific_journal-4118 69 68 3d 3d NUM american_scientific_journal-4118 69 69 plot plot NOUN american_scientific_journal-4118 69 70 ): ): PUNCT american_scientific_journal-4118 69 71 soliton soliton NOUN american_scientific_journal-4118 69 72 profile profile NOUN american_scientific_journal-4118 69 73 of of ADP american_scientific_journal-4118 69 74 ( ( PUNCT american_scientific_journal-4118 69 75 3.11 3.11 NUM american_scientific_journal-4118 69 76 ) ) PUNCT american_scientific_journal-4118 69 77 , , PUNCT american_scientific_journal-4118 69 78 when when SCONJ american_scientific_journal-4118 69 79 𝑙𝑙 𝑙𝑙 PROPN american_scientific_journal-4118 69 80 = = SYM american_scientific_journal-4118 69 81 2 2 NUM american_scientific_journal-4118 69 82 , , PUNCT american_scientific_journal-4118 69 83 π‘Žπ‘Ž π‘Žπ‘Ž NOUN american_scientific_journal-4118 69 84 = = SYM american_scientific_journal-4118 69 85 1 1 NUM american_scientific_journal-4118 69 86 , , PUNCT american_scientific_journal-4118 69 87 𝑏𝑏 𝑏𝑏 NOUN american_scientific_journal-4118 69 88 = = SYM american_scientific_journal-4118 69 89 1 1 NUM american_scientific_journal-4118 69 90 , , PUNCT american_scientific_journal-4118 69 91 𝑐𝑐1 𝑐𝑐1 PROPN american_scientific_journal-4118 70 1 = = SYM american_scientific_journal-4118 70 2 1 1 NUM american_scientific_journal-4118 70 3 american american ADJ american_scientific_journal-4118 70 4 scientific scientific ADJ american_scientific_journal-4118 70 5 research research NOUN american_scientific_journal-4118 70 6 journal journal NOUN american_scientific_journal-4118 70 7 for for ADP american_scientific_journal-4118 70 8 engineering engineering NOUN american_scientific_journal-4118 70 9 , , PUNCT american_scientific_journal-4118 70 10 technology technology NOUN american_scientific_journal-4118 70 11 , , PUNCT american_scientific_journal-4118 70 12 and and CCONJ american_scientific_journal-4118 70 13 sciences science NOUN american_scientific_journal-4118 70 14 ( ( PUNCT american_scientific_journal-4118 70 15 asrjets asrjet NOUN american_scientific_journal-4118 70 16 ) ) PUNCT american_scientific_journal-4118 70 17 ( ( PUNCT american_scientific_journal-4118 70 18 2018 2018 NUM american_scientific_journal-4118 70 19 ) ) PUNCT american_scientific_journal-4118 70 20 volume volume NOUN american_scientific_journal-4118 70 21 44 44 NUM american_scientific_journal-4118 70 22 , , PUNCT american_scientific_journal-4118 70 23 no no DET american_scientific_journal-4118 70 24 1 1 NUM american_scientific_journal-4118 70 25 , , PUNCT american_scientific_journal-4118 70 26 pp pp ADV american_scientific_journal-4118 70 27 58 58 NUM american_scientific_journal-4118 70 28 - - SYM american_scientific_journal-4118 70 29 67 67 NUM american_scientific_journal-4118 70 30 65 65 NUM american_scientific_journal-4118 70 31 singularity singularity NOUN american_scientific_journal-4118 70 32 : : PUNCT american_scientific_journal-4118 70 33 from from ADP american_scientific_journal-4118 70 34 the the DET american_scientific_journal-4118 70 35 above above ADJ american_scientific_journal-4118 70 36 obtained obtain VERB american_scientific_journal-4118 70 37 solutions solution NOUN american_scientific_journal-4118 70 38 we we PRON american_scientific_journal-4118 70 39 observe observe VERB american_scientific_journal-4118 70 40 that that SCONJ american_scientific_journal-4118 70 41 the the DET american_scientific_journal-4118 70 42 solutions solution NOUN american_scientific_journal-4118 70 43 ( ( PUNCT american_scientific_journal-4118 70 44 3.11 3.11 NUM american_scientific_journal-4118 70 45 ) ) PUNCT american_scientific_journal-4118 70 46 have have VERB american_scientific_journal-4118 70 47 singularities singularity NOUN american_scientific_journal-4118 70 48 for for ADP american_scientific_journal-4118 70 49 the the DET american_scientific_journal-4118 70 50 values value NOUN american_scientific_journal-4118 70 51 x x PUNCT american_scientific_journal-4118 70 52 and and CCONJ american_scientific_journal-4118 70 53 t t X american_scientific_journal-4118 70 54 satisfying satisfy VERB american_scientific_journal-4118 70 55 2,0))(1(1 2,0))(1(1 NUM american_scientific_journal-4118 70 56 β‰₯=βˆ’βˆ’Β± β‰₯=βˆ’βˆ’Β± PROPN american_scientific_journal-4118 70 57 nctxnc nctxnc PROPN american_scientific_journal-4118 70 58 . . PUNCT american_scientific_journal-4118 71 1 for for ADP american_scientific_journal-4118 71 2 example example NOUN american_scientific_journal-4118 71 3 , , PUNCT american_scientific_journal-4118 71 4 the the DET american_scientific_journal-4118 71 5 solution solution NOUN american_scientific_journal-4118 71 6 ( ( PUNCT american_scientific_journal-4118 71 7 3.11 3.11 NUM american_scientific_journal-4118 71 8 ) ) PUNCT american_scientific_journal-4118 71 9 has have VERB american_scientific_journal-4118 71 10 a a DET american_scientific_journal-4118 71 11 singularity singularity NOUN american_scientific_journal-4118 71 12 at at ADP american_scientific_journal-4118 71 13 π‘₯π‘₯ π‘₯π‘₯ ADP american_scientific_journal-4118 71 14 = = SYM american_scientific_journal-4118 71 15 βˆ’6 βˆ’6 NOUN american_scientific_journal-4118 71 16 , , PUNCT american_scientific_journal-4118 71 17 when when SCONJ american_scientific_journal-4118 71 18 .1,2,2,81 .1,2,2,81 PUNCT american_scientific_journal-4118 72 1 = = PUNCT american_scientific_journal-4118 72 2 = = SYM american_scientific_journal-4118 72 3 = = NOUN american_scientific_journal-4118 72 4 = = ADJ american_scientific_journal-4118 72 5 tcnc tcnc VERB american_scientific_journal-4118 72 6 figure figure NOUN american_scientific_journal-4118 72 7 3.7 3.7 NUM american_scientific_journal-4118 72 8 : : PUNCT american_scientific_journal-4118 72 9 singularity singularity NOUN american_scientific_journal-4118 72 10 of of ADP american_scientific_journal-4118 72 11 𝑒𝑒1(π‘₯π‘₯ 𝑒𝑒1(π‘₯π‘₯ PROPN american_scientific_journal-4118 72 12 , , PUNCT american_scientific_journal-4118 72 13 𝑑𝑑 𝑑𝑑 PROPN american_scientific_journal-4118 72 14 ) ) PUNCT american_scientific_journal-4118 72 15 at at ADP american_scientific_journal-4118 72 16 π‘₯π‘₯ π‘₯π‘₯ ADP american_scientific_journal-4118 72 17 = = PUNCT american_scientific_journal-4118 72 18 βˆ’6 βˆ’6 NOUN american_scientific_journal-4118 72 19 4 4 NUM american_scientific_journal-4118 72 20 . . PUNCT american_scientific_journal-4118 72 21 results result NOUN american_scientific_journal-4118 72 22 and and CCONJ american_scientific_journal-4118 72 23 discussions discussion NOUN american_scientific_journal-4118 72 24 in in ADP american_scientific_journal-4118 72 25 case case NOUN american_scientific_journal-4118 72 26 of of ADP american_scientific_journal-4118 72 27 our our PRON american_scientific_journal-4118 72 28 proposed propose VERB american_scientific_journal-4118 72 29 method method NOUN american_scientific_journal-4118 72 30 , , PUNCT american_scientific_journal-4118 72 31 we we PRON american_scientific_journal-4118 72 32 have have AUX american_scientific_journal-4118 72 33 got get VERB american_scientific_journal-4118 72 34 many many ADJ american_scientific_journal-4118 72 35 exact exact ADJ american_scientific_journal-4118 72 36 solutions solution NOUN american_scientific_journal-4118 72 37 for for ADP american_scientific_journal-4118 72 38 differetnt differetnt NOUN american_scientific_journal-4118 72 39 values value NOUN american_scientific_journal-4118 72 40 of of ADP american_scientific_journal-4118 72 41 𝑙𝑙. 𝑙𝑙. NOUN american_scientific_journal-4118 72 42 so so SCONJ american_scientific_journal-4118 72 43 we we PRON american_scientific_journal-4118 72 44 will will AUX american_scientific_journal-4118 72 45 discuss discuss VERB american_scientific_journal-4118 72 46 some some DET american_scientific_journal-4118 72 47 solutions solution NOUN american_scientific_journal-4118 72 48 only only ADV american_scientific_journal-4118 72 49 . . PUNCT american_scientific_journal-4118 73 1 equation equation NOUN american_scientific_journal-4118 73 2 ( ( PUNCT american_scientific_journal-4118 73 3 3.8 3.8 NUM american_scientific_journal-4118 73 4 ) ) PUNCT american_scientific_journal-4118 73 5 represents represent VERB american_scientific_journal-4118 73 6 the the DET american_scientific_journal-4118 73 7 soliton soliton NOUN american_scientific_journal-4118 73 8 type type NOUN american_scientific_journal-4118 73 9 solutions solution NOUN american_scientific_journal-4118 73 10 ( ( PUNCT american_scientific_journal-4118 73 11 shown show VERB american_scientific_journal-4118 73 12 in in ADP american_scientific_journal-4118 73 13 figure figure NOUN american_scientific_journal-4118 73 14 3.1(3d 3.1(3d NUM american_scientific_journal-4118 73 15 plot plot NOUN american_scientific_journal-4118 73 16 ) ) PUNCT american_scientific_journal-4118 73 17 and and CCONJ american_scientific_journal-4118 73 18 figure figure VERB american_scientific_journal-4118 73 19 3.4(3d 3.4(3d NUM american_scientific_journal-4118 73 20 plot plot NOUN american_scientific_journal-4118 73 21 ) ) PUNCT american_scientific_journal-4118 73 22 ) ) PUNCT american_scientific_journal-4118 73 23 of of ADP american_scientific_journal-4118 73 24 the the DET american_scientific_journal-4118 73 25 modified modify VERB american_scientific_journal-4118 73 26 liouville liouville NOUN american_scientific_journal-4118 73 27 equation equation NOUN american_scientific_journal-4118 73 28 . . PUNCT american_scientific_journal-4118 74 1 the the DET american_scientific_journal-4118 74 2 corresponding correspond VERB american_scientific_journal-4118 74 3 two two NUM american_scientific_journal-4118 74 4 - - PUNCT american_scientific_journal-4118 74 5 dimensional dimensional ADJ american_scientific_journal-4118 74 6 plot plot NOUN american_scientific_journal-4118 74 7 are be AUX american_scientific_journal-4118 74 8 given give VERB american_scientific_journal-4118 74 9 in in ADP american_scientific_journal-4118 74 10 figure figure NOUN american_scientific_journal-4118 74 11 3.2(2d 3.2(2d NUM american_scientific_journal-4118 74 12 plot plot NOUN american_scientific_journal-4118 74 13 ) ) PUNCT american_scientific_journal-4118 74 14 and and CCONJ american_scientific_journal-4118 74 15 figure figure VERB american_scientific_journal-4118 74 16 3.4(2d 3.4(2d NUM american_scientific_journal-4118 74 17 plot plot NOUN american_scientific_journal-4118 74 18 ) ) PUNCT american_scientific_journal-4118 74 19 respectively respectively ADV american_scientific_journal-4118 74 20 . . PUNCT american_scientific_journal-4118 74 21 and and CCONJ american_scientific_journal-4118 74 22 finally finally ADV american_scientific_journal-4118 74 23 figure figure VERB american_scientific_journal-4118 74 24 3.5(3d 3.5(3d NUM american_scientific_journal-4118 74 25 plot plot NOUN american_scientific_journal-4118 74 26 ) ) PUNCT american_scientific_journal-4118 74 27 and and CCONJ american_scientific_journal-4118 74 28 figure figure VERB american_scientific_journal-4118 74 29 3.6(3d 3.6(3d NUM american_scientific_journal-4118 74 30 plot plot NOUN american_scientific_journal-4118 74 31 ) ) PUNCT american_scientific_journal-4118 74 32 give give VERB american_scientific_journal-4118 74 33 also also ADV american_scientific_journal-4118 74 34 the the DET american_scientific_journal-4118 74 35 soliton soliton NOUN american_scientific_journal-4118 74 36 profile profile NOUN american_scientific_journal-4118 74 37 for for ADP american_scientific_journal-4118 74 38 the the DET american_scientific_journal-4118 74 39 solutions solution NOUN american_scientific_journal-4118 74 40 of of ADP american_scientific_journal-4118 74 41 the the DET american_scientific_journal-4118 74 42 equation equation NOUN american_scientific_journal-4118 74 43 regularized regularize VERB american_scientific_journal-4118 74 44 long long ADJ american_scientific_journal-4118 74 45 wave wave NOUN american_scientific_journal-4118 74 46 equation equation NOUN american_scientific_journal-4118 74 47 where where SCONJ american_scientific_journal-4118 74 48 the the DET american_scientific_journal-4118 74 49 waves wave NOUN american_scientific_journal-4118 74 50 move move VERB american_scientific_journal-4118 74 51 with with ADP american_scientific_journal-4118 74 52 2 2 NUM american_scientific_journal-4118 74 53 and and CCONJ american_scientific_journal-4118 74 54 3 3 NUM american_scientific_journal-4118 74 55 respectively respectively ADV american_scientific_journal-4118 74 56 . . PUNCT american_scientific_journal-4118 75 1 a a DET american_scientific_journal-4118 75 2 singularity singularity NOUN american_scientific_journal-4118 75 3 has have AUX american_scientific_journal-4118 75 4 been be AUX american_scientific_journal-4118 75 5 shown show VERB american_scientific_journal-4118 75 6 in in ADP american_scientific_journal-4118 75 7 figure figure NOUN american_scientific_journal-4118 75 8 3.7 3.7 NUM american_scientific_journal-4118 75 9 . . PUNCT american_scientific_journal-4118 76 1 5 5 NUM american_scientific_journal-4118 76 2 . . X american_scientific_journal-4118 76 3 conclusion conclusion VERB american_scientific_journal-4118 76 4 the the DET american_scientific_journal-4118 76 5 main main ADJ american_scientific_journal-4118 76 6 achievement achievement NOUN american_scientific_journal-4118 76 7 of of ADP american_scientific_journal-4118 76 8 this this DET american_scientific_journal-4118 76 9 work work NOUN american_scientific_journal-4118 76 10 is be AUX american_scientific_journal-4118 76 11 to to PART american_scientific_journal-4118 76 12 explore explore VERB american_scientific_journal-4118 76 13 a a DET american_scientific_journal-4118 76 14 new new ADJ american_scientific_journal-4118 76 15 approach approach NOUN american_scientific_journal-4118 76 16 of of ADP american_scientific_journal-4118 76 17 the the DET american_scientific_journal-4118 76 18 bernoulli bernoulli PROPN american_scientific_journal-4118 76 19 sub sub ADJ american_scientific_journal-4118 76 20 - - ADJ american_scientific_journal-4118 76 21 ode ode ADJ american_scientific_journal-4118 76 22 method method NOUN american_scientific_journal-4118 76 23 , , PUNCT american_scientific_journal-4118 76 24 which which PRON american_scientific_journal-4118 76 25 is be AUX american_scientific_journal-4118 76 26 capable capable ADJ american_scientific_journal-4118 76 27 of of ADP american_scientific_journal-4118 76 28 producing produce VERB american_scientific_journal-4118 76 29 more more ADV american_scientific_journal-4118 76 30 fruitful fruitful ADJ american_scientific_journal-4118 76 31 and and CCONJ american_scientific_journal-4118 76 32 new new ADJ american_scientific_journal-4118 76 33 solitary solitary ADJ american_scientific_journal-4118 76 34 wave wave NOUN american_scientific_journal-4118 76 35 solutions solution NOUN american_scientific_journal-4118 76 36 of of ADP american_scientific_journal-4118 76 37 several several ADJ american_scientific_journal-4118 76 38 nonlinear nonlinear ADJ american_scientific_journal-4118 76 39 evolution evolution NOUN american_scientific_journal-4118 76 40 equations equation NOUN american_scientific_journal-4118 76 41 . . PUNCT american_scientific_journal-4118 77 1 using use VERB american_scientific_journal-4118 77 2 this this DET american_scientific_journal-4118 77 3 method method NOUN american_scientific_journal-4118 77 4 , , PUNCT american_scientific_journal-4118 77 5 we we PRON american_scientific_journal-4118 77 6 have have AUX american_scientific_journal-4118 77 7 successfully successfully ADV american_scientific_journal-4118 77 8 obtained obtain VERB american_scientific_journal-4118 77 9 exact exact ADJ american_scientific_journal-4118 77 10 solutions solution NOUN american_scientific_journal-4118 77 11 and and CCONJ american_scientific_journal-4118 77 12 then then ADV american_scientific_journal-4118 77 13 solitary solitary ADJ american_scientific_journal-4118 77 14 wave wave NOUN american_scientific_journal-4118 77 15 solutions solution NOUN american_scientific_journal-4118 77 16 in in ADP american_scientific_journal-4118 77 17 terms term NOUN american_scientific_journal-4118 77 18 of of ADP american_scientific_journal-4118 77 19 fractional fractional ADJ american_scientific_journal-4118 77 20 functions function NOUN american_scientific_journal-4118 77 21 . . PUNCT american_scientific_journal-4118 78 1 besides besides SCONJ american_scientific_journal-4118 78 2 , , PUNCT american_scientific_journal-4118 78 3 there there PRON american_scientific_journal-4118 78 4 are be VERB american_scientific_journal-4118 78 5 several several ADJ american_scientific_journal-4118 78 6 avenues avenue NOUN american_scientific_journal-4118 78 7 for for ADP american_scientific_journal-4118 78 8 further further ADJ american_scientific_journal-4118 78 9 investigation investigation NOUN american_scientific_journal-4118 78 10 : : PUNCT american_scientific_journal-4118 78 11 οƒ˜ οƒ˜ VERB american_scientific_journal-4118 78 12 seeking seek VERB american_scientific_journal-4118 78 13 exact exact ADJ american_scientific_journal-4118 78 14 solutions solution NOUN american_scientific_journal-4118 78 15 to to ADP american_scientific_journal-4118 78 16 nees nee NOUN american_scientific_journal-4118 78 17 having have VERB american_scientific_journal-4118 78 18 ( ( PUNCT american_scientific_journal-4118 78 19 2 2 NUM american_scientific_journal-4118 78 20 + + NOUN american_scientific_journal-4118 78 21 1 1 NUM american_scientific_journal-4118 78 22 ) ) PUNCT american_scientific_journal-4118 78 23 or or CCONJ american_scientific_journal-4118 78 24 ( ( PUNCT american_scientific_journal-4118 78 25 3 3 NUM american_scientific_journal-4118 78 26 + + NOUN american_scientific_journal-4118 78 27 1 1 NUM american_scientific_journal-4118 78 28 ) ) PUNCT american_scientific_journal-4118 78 29 dimension dimension NOUN american_scientific_journal-4118 78 30 through through ADP american_scientific_journal-4118 78 31 the the DET american_scientific_journal-4118 78 32 proposed propose VERB american_scientific_journal-4118 78 33 method method NOUN american_scientific_journal-4118 78 34 is be AUX american_scientific_journal-4118 78 35 another another DET american_scientific_journal-4118 78 36 possible possible ADJ american_scientific_journal-4118 78 37 study study NOUN american_scientific_journal-4118 78 38 . . PUNCT american_scientific_journal-4118 79 1 οƒ˜ οƒ˜ ADJ american_scientific_journal-4118 79 2 applications application NOUN american_scientific_journal-4118 79 3 of of ADP american_scientific_journal-4118 79 4 the the DET american_scientific_journal-4118 79 5 obtained obtain VERB american_scientific_journal-4118 79 6 solutions solution NOUN american_scientific_journal-4118 79 7 can can AUX american_scientific_journal-4118 79 8 be be AUX american_scientific_journal-4118 79 9 discussed discuss VERB american_scientific_journal-4118 79 10 . . PUNCT american_scientific_journal-4118 80 1 references reference NOUN american_scientific_journal-4118 80 2 [ [ X american_scientific_journal-4118 80 3 1 1 NUM american_scientific_journal-4118 80 4 ] ] PUNCT american_scientific_journal-4118 80 5 . . PUNCT american_scientific_journal-4118 81 1 abdou abdou PROPN american_scientific_journal-4118 81 2 m. m. PROPN american_scientific_journal-4118 81 3 a. a. PROPN american_scientific_journal-4118 81 4 , , PUNCT american_scientific_journal-4118 81 5 the the DET american_scientific_journal-4118 81 6 extended extended ADJ american_scientific_journal-4118 81 7 tanh tanh NOUN american_scientific_journal-4118 81 8 - - PUNCT american_scientific_journal-4118 81 9 method method NOUN american_scientific_journal-4118 81 10 and and CCONJ american_scientific_journal-4118 81 11 its its PRON american_scientific_journal-4118 81 12 applications application NOUN american_scientific_journal-4118 81 13 for for ADP american_scientific_journal-4118 81 14 solving solve VERB american_scientific_journal-4118 81 15 nonlinear nonlinear ADJ american_scientific_journal-4118 81 16 physical physical ADJ american_scientific_journal-4118 81 17 models model NOUN american_scientific_journal-4118 81 18 , , PUNCT american_scientific_journal-4118 81 19 appl appl PROPN american_scientific_journal-4118 81 20 . . PROPN american_scientific_journal-4118 81 21 math math PROPN american_scientific_journal-4118 81 22 . . PUNCT american_scientific_journal-4118 82 1 comput comput NOUN american_scientific_journal-4118 82 2 . . PUNCT american_scientific_journal-4118 82 3 , , PUNCT american_scientific_journal-4118 82 4 190 190 NUM american_scientific_journal-4118 82 5 ( ( PUNCT american_scientific_journal-4118 82 6 2007 2007 NUM american_scientific_journal-4118 82 7 ) ) PUNCT american_scientific_journal-4118 82 8 , , PUNCT american_scientific_journal-4118 82 9 988 988 NUM american_scientific_journal-4118 82 10 - - SYM american_scientific_journal-4118 82 11 996 996 NUM american_scientific_journal-4118 82 12 . . PUNCT american_scientific_journal-4118 83 1 [ [ X american_scientific_journal-4118 83 2 2 2 NUM american_scientific_journal-4118 83 3 ] ] PUNCT american_scientific_journal-4118 83 4 . . PUNCT american_scientific_journal-4118 84 1 malfliet malfliet PROPN american_scientific_journal-4118 84 2 w. w. PROPN american_scientific_journal-4118 84 3 , , PUNCT american_scientific_journal-4118 84 4 solitory solitory NOUN american_scientific_journal-4118 84 5 wave wave NOUN american_scientific_journal-4118 84 6 solutions solution NOUN american_scientific_journal-4118 84 7 of of ADP american_scientific_journal-4118 84 8 nonlinear nonlinear ADJ american_scientific_journal-4118 84 9 wave wave NOUN american_scientific_journal-4118 84 10 equations equation NOUN american_scientific_journal-4118 84 11 , , PUNCT american_scientific_journal-4118 84 12 am be AUX american_scientific_journal-4118 84 13 . . PUNCT american_scientific_journal-4118 85 1 j. j. PROPN american_scientific_journal-4118 85 2 phys phys PROPN american_scientific_journal-4118 85 3 . . PUNCT american_scientific_journal-4118 85 4 ,60(1992 ,60(1992 PUNCT american_scientific_journal-4118 85 5 ) ) PUNCT american_scientific_journal-4118 85 6 , , PUNCT american_scientific_journal-4118 85 7 650–654 650–654 NUM american_scientific_journal-4118 85 8 . . PUNCT american_scientific_journal-4118 86 1 american american ADJ american_scientific_journal-4118 86 2 scientific scientific ADJ american_scientific_journal-4118 86 3 research research PROPN american_scientific_journal-4118 86 4 journal journal NOUN american_scientific_journal-4118 86 5 for for ADP american_scientific_journal-4118 86 6 engineering engineering NOUN american_scientific_journal-4118 86 7 , , PUNCT american_scientific_journal-4118 86 8 technology technology NOUN american_scientific_journal-4118 86 9 , , PUNCT american_scientific_journal-4118 86 10 and and CCONJ american_scientific_journal-4118 86 11 sciences science NOUN american_scientific_journal-4118 86 12 ( ( PUNCT american_scientific_journal-4118 86 13 asrjets asrjet NOUN american_scientific_journal-4118 86 14 ) ) PUNCT american_scientific_journal-4118 86 15 ( ( PUNCT american_scientific_journal-4118 86 16 2018 2018 NUM american_scientific_journal-4118 86 17 ) ) PUNCT american_scientific_journal-4118 86 18 volume volume NOUN american_scientific_journal-4118 86 19 44 44 NUM american_scientific_journal-4118 86 20 , , PUNCT american_scientific_journal-4118 86 21 no no DET american_scientific_journal-4118 86 22 1 1 NUM american_scientific_journal-4118 86 23 , , PUNCT american_scientific_journal-4118 86 24 pp pp ADV american_scientific_journal-4118 86 25 58 58 NUM american_scientific_journal-4118 86 26 - - SYM american_scientific_journal-4118 86 27 67 67 NUM american_scientific_journal-4118 86 28 66 66 NUM american_scientific_journal-4118 87 1 [ [ X american_scientific_journal-4118 87 2 3 3 NUM american_scientific_journal-4118 87 3 ] ] PUNCT american_scientific_journal-4118 87 4 . . PUNCT american_scientific_journal-4118 88 1 hereman hereman PROPN american_scientific_journal-4118 88 2 w. w. PROPN american_scientific_journal-4118 88 3 and and CCONJ american_scientific_journal-4118 88 4 malfliet malfliet PROPN american_scientific_journal-4118 88 5 w. w. PROPN american_scientific_journal-4118 88 6 , , PUNCT american_scientific_journal-4118 88 7 the the DET american_scientific_journal-4118 88 8 tanh tanh PROPN american_scientific_journal-4118 88 9 method method NOUN american_scientific_journal-4118 88 10 i i PRON american_scientific_journal-4118 88 11 : : PUNCT american_scientific_journal-4118 88 12 exact exact ADJ american_scientific_journal-4118 88 13 solutions solution NOUN american_scientific_journal-4118 88 14 of of ADP american_scientific_journal-4118 88 15 nonlinear nonlinear ADJ american_scientific_journal-4118 88 16 evolution evolution NOUN american_scientific_journal-4118 88 17 and and CCONJ american_scientific_journal-4118 88 18 wave wave NOUN american_scientific_journal-4118 88 19 equations equation NOUN american_scientific_journal-4118 88 20 , , PUNCT american_scientific_journal-4118 88 21 phys phy NOUN american_scientific_journal-4118 88 22 . . PUNCT american_scientific_journal-4118 88 23 scripta scripta PROPN american_scientific_journal-4118 88 24 , , PUNCT american_scientific_journal-4118 88 25 54(1996 54(1996 NUM american_scientific_journal-4118 88 26 ) ) PUNCT american_scientific_journal-4118 88 27 , , PUNCT american_scientific_journal-4118 88 28 563–568 563–568 NUM american_scientific_journal-4118 88 29 . . PUNCT american_scientific_journal-4118 89 1 [ [ X american_scientific_journal-4118 89 2 4 4 NUM american_scientific_journal-4118 89 3 ] ] PUNCT american_scientific_journal-4118 89 4 . . PUNCT american_scientific_journal-4118 90 1 wazwaz wazwaz PROPN american_scientific_journal-4118 90 2 a. a. NOUN american_scientific_journal-4118 90 3 m. m. NOUN american_scientific_journal-4118 90 4 , , PUNCT american_scientific_journal-4118 90 5 the the DET american_scientific_journal-4118 90 6 tanh tanh PROPN american_scientific_journal-4118 90 7 method method NOUN american_scientific_journal-4118 90 8 : : PUNCT american_scientific_journal-4118 90 9 solitons soliton NOUN american_scientific_journal-4118 90 10 and and CCONJ american_scientific_journal-4118 90 11 periodic periodic ADJ american_scientific_journal-4118 90 12 solutions solution NOUN american_scientific_journal-4118 90 13 for for ADP american_scientific_journal-4118 90 14 the the DET american_scientific_journal-4118 90 15 dodd dodd NOUN american_scientific_journal-4118 90 16 - - PUNCT american_scientific_journal-4118 90 17 bullough bullough NOUN american_scientific_journal-4118 90 18 - - PUNCT american_scientific_journal-4118 90 19 mikhailov mikhailov NOUN american_scientific_journal-4118 90 20 and and CCONJ american_scientific_journal-4118 90 21 the the DET american_scientific_journal-4118 90 22 tzitzeica tzitzeica PROPN american_scientific_journal-4118 90 23 - - PUNCT american_scientific_journal-4118 90 24 dodd dodd NOUN american_scientific_journal-4118 90 25 - - PUNCT american_scientific_journal-4118 90 26 bullough bullough NOUN american_scientific_journal-4118 90 27 equations equation NOUN american_scientific_journal-4118 90 28 , , PUNCT american_scientific_journal-4118 90 29 chaos chaos NOUN american_scientific_journal-4118 90 30 soliton soliton NOUN american_scientific_journal-4118 90 31 fractal fractal NOUN american_scientific_journal-4118 90 32 , , PUNCT american_scientific_journal-4118 90 33 25(2005 25(2005 NUM american_scientific_journal-4118 90 34 ) ) PUNCT american_scientific_journal-4118 90 35 , , PUNCT american_scientific_journal-4118 90 36 55–63 55–63 NUM american_scientific_journal-4118 90 37 . . PUNCT american_scientific_journal-4118 91 1 [ [ X american_scientific_journal-4118 91 2 5 5 NUM american_scientific_journal-4118 91 3 ] ] PUNCT american_scientific_journal-4118 91 4 . . PUNCT american_scientific_journal-4118 92 1 wazwaz wazwaz PROPN american_scientific_journal-4118 92 2 a. a. NOUN american_scientific_journal-4118 92 3 m. m. NOUN american_scientific_journal-4118 92 4 , , PUNCT american_scientific_journal-4118 92 5 the the DET american_scientific_journal-4118 92 6 extended extended ADJ american_scientific_journal-4118 92 7 tanh tanh NOUN american_scientific_journal-4118 92 8 method method NOUN american_scientific_journal-4118 92 9 for for ADP american_scientific_journal-4118 92 10 new new ADJ american_scientific_journal-4118 92 11 soliton soliton NOUN american_scientific_journal-4118 92 12 solutions solution NOUN american_scientific_journal-4118 92 13 for for ADP american_scientific_journal-4118 92 14 many many ADJ american_scientific_journal-4118 92 15 forms form NOUN american_scientific_journal-4118 92 16 of of ADP american_scientific_journal-4118 92 17 the the DET american_scientific_journal-4118 92 18 fifth fifth ADJ american_scientific_journal-4118 92 19 - - PUNCT american_scientific_journal-4118 92 20 order order NOUN american_scientific_journal-4118 92 21 kdv kdv NOUN american_scientific_journal-4118 92 22 equations equation NOUN american_scientific_journal-4118 92 23 , , PUNCT american_scientific_journal-4118 92 24 appli appli PROPN american_scientific_journal-4118 92 25 . . PUNCT american_scientific_journal-4118 92 26 math math PROPN american_scientific_journal-4118 92 27 . . PUNCT american_scientific_journal-4118 93 1 comput comput NOUN american_scientific_journal-4118 93 2 . . PUNCT american_scientific_journal-4118 94 1 184(2007 184(2007 NUM american_scientific_journal-4118 94 2 ) ) PUNCT american_scientific_journal-4118 94 3 , , PUNCT american_scientific_journal-4118 94 4 1002–1014 1002–1014 NUM american_scientific_journal-4118 94 5 . . PUNCT american_scientific_journal-4118 95 1 [ [ X american_scientific_journal-4118 95 2 6 6 NUM american_scientific_journal-4118 95 3 ] ] PUNCT american_scientific_journal-4118 95 4 . . PUNCT american_scientific_journal-4118 96 1 chen chen PROPN american_scientific_journal-4118 96 2 y. y. PROPN american_scientific_journal-4118 96 3 , , PUNCT american_scientific_journal-4118 96 4 wang wang PROPN american_scientific_journal-4118 96 5 q. q. PROPN american_scientific_journal-4118 96 6 , , PUNCT american_scientific_journal-4118 96 7 extended extend VERB american_scientific_journal-4118 96 8 jacobi jacobi PROPN american_scientific_journal-4118 96 9 elliptic elliptic ADJ american_scientific_journal-4118 96 10 function function NOUN american_scientific_journal-4118 96 11 rational rational ADJ american_scientific_journal-4118 96 12 expansion expansion NOUN american_scientific_journal-4118 96 13 method method NOUN american_scientific_journal-4118 96 14 and and CCONJ american_scientific_journal-4118 96 15 abundant abundant ADJ american_scientific_journal-4118 96 16 families family NOUN american_scientific_journal-4118 96 17 of of ADP american_scientific_journal-4118 96 18 jacobi jacobi PROPN american_scientific_journal-4118 96 19 elliptic elliptic PROPN american_scientific_journal-4118 96 20 functions function NOUN american_scientific_journal-4118 96 21 solutions solution NOUN american_scientific_journal-4118 96 22 to to ADP american_scientific_journal-4118 96 23 the the DET american_scientific_journal-4118 96 24 ( ( PUNCT american_scientific_journal-4118 96 25 1 1 NUM american_scientific_journal-4118 96 26 + + NOUN american_scientific_journal-4118 96 27 1)dimensional 1)dimensional NUM american_scientific_journal-4118 96 28 nonlinear nonlinear ADJ american_scientific_journal-4118 96 29 dispersive dispersive ADJ american_scientific_journal-4118 96 30 long long ADJ american_scientific_journal-4118 96 31 wave wave NOUN american_scientific_journal-4118 96 32 equation equation NOUN american_scientific_journal-4118 96 33 . . PUNCT american_scientific_journal-4118 97 1 chaos chaos NOUN american_scientific_journal-4118 97 2 , , PUNCT american_scientific_journal-4118 97 3 solitons soliton NOUN american_scientific_journal-4118 97 4 & & CCONJ american_scientific_journal-4118 97 5 fractals fractal NOUN american_scientific_journal-4118 97 6 . . PUNCT american_scientific_journal-4118 98 1 24(2005 24(2005 NUM american_scientific_journal-4118 98 2 ): ): PUNCT american_scientific_journal-4118 98 3 745 745 NUM american_scientific_journal-4118 98 4 - - SYM american_scientific_journal-4118 98 5 757 757 NUM american_scientific_journal-4118 98 6 . . PUNCT american_scientific_journal-4118 99 1 [ [ X american_scientific_journal-4118 99 2 7 7 NUM american_scientific_journal-4118 99 3 ] ] PUNCT american_scientific_journal-4118 99 4 . . PUNCT american_scientific_journal-4118 100 1 li li PROPN american_scientific_journal-4118 100 2 z. z. PROPN american_scientific_journal-4118 100 3 , , PUNCT american_scientific_journal-4118 100 4 wang wang PROPN american_scientific_journal-4118 100 5 m. m. PROPN american_scientific_journal-4118 100 6 l. l. PROPN american_scientific_journal-4118 100 7 , , PUNCT american_scientific_journal-4118 100 8 a a DET american_scientific_journal-4118 100 9 sub sub ADJ american_scientific_journal-4118 100 10 - - ADJ american_scientific_journal-4118 100 11 ode ode ADJ american_scientific_journal-4118 100 12 method method NOUN american_scientific_journal-4118 100 13 for for ADP american_scientific_journal-4118 100 14 finding find VERB american_scientific_journal-4118 100 15 exact exact ADJ american_scientific_journal-4118 100 16 solutions solution NOUN american_scientific_journal-4118 100 17 of of ADP american_scientific_journal-4118 100 18 a a DET american_scientific_journal-4118 100 19 generalized generalized ADJ american_scientific_journal-4118 100 20 kdv kdv NOUN american_scientific_journal-4118 100 21 - - PUNCT american_scientific_journal-4118 100 22 mkdv mkdv NOUN american_scientific_journal-4118 100 23 equation equation NOUN american_scientific_journal-4118 100 24 with with ADP american_scientific_journal-4118 100 25 higher high ADJ american_scientific_journal-4118 100 26 order order NOUN american_scientific_journal-4118 100 27 nonlinear nonlinear ADJ american_scientific_journal-4118 100 28 terms term NOUN american_scientific_journal-4118 100 29 . . PUNCT american_scientific_journal-4118 101 1 phys phy NOUN american_scientific_journal-4118 101 2 . . PUNCT american_scientific_journal-4118 102 1 lett lett PROPN american_scientific_journal-4118 102 2 . . PUNCT american_scientific_journal-4118 103 1 a. a. PROPN american_scientific_journal-4118 103 2 361(2007 361(2007 PROPN american_scientific_journal-4118 103 3 ): ): PUNCT american_scientific_journal-4118 103 4 115 115 NUM american_scientific_journal-4118 103 5 - - SYM american_scientific_journal-4118 103 6 118 118 NUM american_scientific_journal-4118 103 7 . . PUNCT american_scientific_journal-4118 104 1 [ [ X american_scientific_journal-4118 104 2 8 8 NUM american_scientific_journal-4118 104 3 ] ] PUNCT american_scientific_journal-4118 104 4 . . PUNCT american_scientific_journal-4118 105 1 yan yan PROPN american_scientific_journal-4118 105 2 z. z. PROPN american_scientific_journal-4118 105 3 , , PUNCT american_scientific_journal-4118 105 4 abundant abundant ADJ american_scientific_journal-4118 105 5 families family NOUN american_scientific_journal-4118 105 6 of of ADP american_scientific_journal-4118 105 7 jacobi jacobi PROPN american_scientific_journal-4118 105 8 elliptic elliptic ADJ american_scientific_journal-4118 105 9 functions function NOUN american_scientific_journal-4118 105 10 of of ADP american_scientific_journal-4118 105 11 the the DET american_scientific_journal-4118 105 12 ( ( PUNCT american_scientific_journal-4118 105 13 2 2 NUM american_scientific_journal-4118 105 14 + + NOUN american_scientific_journal-4118 105 15 1)-dimensional 1)-dimensional ADJ american_scientific_journal-4118 105 16 integrable integrable ADJ american_scientific_journal-4118 105 17 davey davey NOUN american_scientific_journal-4118 105 18 stawartson stawartson NOUN american_scientific_journal-4118 105 19 - - PUNCT american_scientific_journal-4118 105 20 type type NOUN american_scientific_journal-4118 105 21 equation equation NOUN american_scientific_journal-4118 105 22 via via ADP american_scientific_journal-4118 105 23 a a DET american_scientific_journal-4118 105 24 new new ADJ american_scientific_journal-4118 105 25 method method NOUN american_scientific_journal-4118 105 26 . . PUNCT american_scientific_journal-4118 106 1 chaos chaos NOUN american_scientific_journal-4118 106 2 , , PUNCT american_scientific_journal-4118 106 3 solitons soliton NOUN american_scientific_journal-4118 106 4 & & CCONJ american_scientific_journal-4118 106 5 fractals fractal NOUN american_scientific_journal-4118 106 6 . . PUNCT american_scientific_journal-4118 107 1 18(2003 18(2003 NUM american_scientific_journal-4118 107 2 ): ): PUNCT american_scientific_journal-4118 107 3 299 299 NUM american_scientific_journal-4118 107 4 - - NUM american_scientific_journal-4118 107 5 309 309 NUM american_scientific_journal-4118 107 6 . . PUNCT american_scientific_journal-4118 108 1 [ [ X american_scientific_journal-4118 108 2 9 9 NUM american_scientific_journal-4118 108 3 ] ] PUNCT american_scientific_journal-4118 108 4 . . PUNCT american_scientific_journal-4118 109 1 boiti boiti PROPN american_scientific_journal-4118 109 2 m. m. PROPN american_scientific_journal-4118 109 3 , , PUNCT american_scientific_journal-4118 109 4 leon leon PROPN american_scientific_journal-4118 109 5 j. j. PROPN american_scientific_journal-4118 109 6 , , PUNCT american_scientific_journal-4118 109 7 pempinelli pempinelli PROPN american_scientific_journal-4118 109 8 p. p. PROPN american_scientific_journal-4118 109 9 , , PUNCT american_scientific_journal-4118 109 10 spectral spectral ADJ american_scientific_journal-4118 109 11 transform transform VERB american_scientific_journal-4118 109 12 for for ADP american_scientific_journal-4118 109 13 a a DET american_scientific_journal-4118 109 14 two two NUM american_scientific_journal-4118 109 15 spatial spatial ADJ american_scientific_journal-4118 109 16 dimension dimension NOUN american_scientific_journal-4118 109 17 extension extension NOUN american_scientific_journal-4118 109 18 of of ADP american_scientific_journal-4118 109 19 the the DET american_scientific_journal-4118 109 20 dispersive dispersive ADJ american_scientific_journal-4118 109 21 long long ADJ american_scientific_journal-4118 109 22 wave wave NOUN american_scientific_journal-4118 109 23 equation equation NOUN american_scientific_journal-4118 109 24 . . PUNCT american_scientific_journal-4118 110 1 inverse inverse PROPN american_scientific_journal-4118 110 2 probl probl NOUN american_scientific_journal-4118 110 3 . . PUNCT american_scientific_journal-4118 111 1 3(1987 3(1987 NUM american_scientific_journal-4118 111 2 ): ): PUNCT american_scientific_journal-4118 111 3 371 371 NUM american_scientific_journal-4118 111 4 - - SYM american_scientific_journal-4118 111 5 387 387 NUM american_scientific_journal-4118 111 6 . . PUNCT american_scientific_journal-4118 112 1 [ [ X american_scientific_journal-4118 112 2 10 10 NUM american_scientific_journal-4118 112 3 ] ] PUNCT american_scientific_journal-4118 112 4 . . PUNCT american_scientific_journal-4118 113 1 miura miura PROPN american_scientific_journal-4118 113 2 m. m. PROPN american_scientific_journal-4118 113 3 r r PROPN american_scientific_journal-4118 113 4 , , PUNCT american_scientific_journal-4118 113 5 backlund backlund PROPN american_scientific_journal-4118 113 6 transformation transformation NOUN american_scientific_journal-4118 113 7 . . PUNCT american_scientific_journal-4118 114 1 springer springer NOUN american_scientific_journal-4118 114 2 , , PUNCT american_scientific_journal-4118 114 3 berlin berlin PROPN american_scientific_journal-4118 114 4 , , PUNCT american_scientific_journal-4118 114 5 ( ( PUNCT american_scientific_journal-4118 114 6 1978 1978 NUM american_scientific_journal-4118 114 7 ) ) PUNCT american_scientific_journal-4118 115 1 [ [ X american_scientific_journal-4118 115 2 11 11 NUM american_scientific_journal-4118 115 3 ] ] PUNCT american_scientific_journal-4118 115 4 . . PUNCT american_scientific_journal-4118 116 1 ren ren PROPN american_scientific_journal-4118 116 2 y. y. PROPN american_scientific_journal-4118 116 3 , , PUNCT american_scientific_journal-4118 116 4 zhang zhang PROPN american_scientific_journal-4118 116 5 h. h. PROPN american_scientific_journal-4118 116 6 , , PUNCT american_scientific_journal-4118 116 7 new new ADJ american_scientific_journal-4118 116 8 generalized generalized ADJ american_scientific_journal-4118 116 9 hyperbolic hyperbolic ADJ american_scientific_journal-4118 116 10 functions function NOUN american_scientific_journal-4118 116 11 and and CCONJ american_scientific_journal-4118 116 12 auto auto NOUN american_scientific_journal-4118 116 13 - - PUNCT american_scientific_journal-4118 116 14 backlund backlund NOUN american_scientific_journal-4118 116 15 transformation transformation NOUN american_scientific_journal-4118 116 16 to to PART american_scientific_journal-4118 116 17 find find VERB american_scientific_journal-4118 116 18 exact exact ADJ american_scientific_journal-4118 116 19 solutions solution NOUN american_scientific_journal-4118 116 20 of of ADP american_scientific_journal-4118 116 21 the the DET american_scientific_journal-4118 116 22 ( ( PUNCT american_scientific_journal-4118 116 23 2 2 NUM american_scientific_journal-4118 116 24 + + NOUN american_scientific_journal-4118 116 25 1)-dimensional 1)-dimensional ADJ american_scientific_journal-4118 116 26 nny nny ADJ american_scientific_journal-4118 116 27 equation equation NOUN american_scientific_journal-4118 116 28 . . PUNCT american_scientific_journal-4118 117 1 phys phy NOUN american_scientific_journal-4118 117 2 . . PUNCT american_scientific_journal-4118 118 1 lett lett PROPN american_scientific_journal-4118 118 2 . . PUNCT american_scientific_journal-4118 119 1 a. a. PROPN american_scientific_journal-4118 119 2 357(2006 357(2006 NUM american_scientific_journal-4118 119 3 ): ): PUNCT american_scientific_journal-4118 119 4 438 438 NUM american_scientific_journal-4118 119 5 - - SYM american_scientific_journal-4118 119 6 448 448 NUM american_scientific_journal-4118 119 7 . . PUNCT american_scientific_journal-4118 120 1 [ [ X american_scientific_journal-4118 120 2 12 12 NUM american_scientific_journal-4118 120 3 ] ] PUNCT american_scientific_journal-4118 120 4 . . PUNCT american_scientific_journal-4118 121 1 rogers rogers PROPN american_scientific_journal-4118 121 2 c. c. PROPN american_scientific_journal-4118 121 3 , , PUNCT american_scientific_journal-4118 121 4 shadwick shadwick PROPN american_scientific_journal-4118 121 5 w. w. PROPN american_scientific_journal-4118 121 6 f. f. PROPN american_scientific_journal-4118 121 7 , , PUNCT american_scientific_journal-4118 121 8 backlund backlund PROPN american_scientific_journal-4118 121 9 transformation transformation NOUN american_scientific_journal-4118 121 10 . . PUNCT american_scientific_journal-4118 122 1 academic academic ADJ american_scientific_journal-4118 122 2 press press NOUN american_scientific_journal-4118 122 3 , , PUNCT american_scientific_journal-4118 122 4 new new PROPN american_scientific_journal-4118 122 5 york york PROPN american_scientific_journal-4118 122 6 , , PUNCT american_scientific_journal-4118 122 7 ( ( PUNCT american_scientific_journal-4118 122 8 1982 1982 NUM american_scientific_journal-4118 122 9 ) ) PUNCT american_scientific_journal-4118 123 1 [ [ X american_scientific_journal-4118 123 2 13 13 NUM american_scientific_journal-4118 123 3 ] ] PUNCT american_scientific_journal-4118 123 4 . . PUNCT american_scientific_journal-4118 124 1 moussa moussa PROPN american_scientific_journal-4118 124 2 m. m. PROPN american_scientific_journal-4118 124 3 h. h. PROPN american_scientific_journal-4118 124 4 m. m. PROPN american_scientific_journal-4118 124 5 , , PUNCT american_scientific_journal-4118 124 6 elshikh elshikh PROPN american_scientific_journal-4118 124 7 r. r. PROPN american_scientific_journal-4118 124 8 m. m. PROPN american_scientific_journal-4118 124 9 , , PUNCT american_scientific_journal-4118 124 10 two two NUM american_scientific_journal-4118 124 11 applications application NOUN american_scientific_journal-4118 124 12 of of ADP american_scientific_journal-4118 124 13 the the DET american_scientific_journal-4118 124 14 homogeneous homogeneous ADJ american_scientific_journal-4118 124 15 balance balance NOUN american_scientific_journal-4118 124 16 method method NOUN american_scientific_journal-4118 124 17 for for ADP american_scientific_journal-4118 124 18 solving solve VERB american_scientific_journal-4118 124 19 the the DET american_scientific_journal-4118 124 20 generalized generalize VERB american_scientific_journal-4118 124 21 hirota hirota NOUN american_scientific_journal-4118 124 22 - - PUNCT american_scientific_journal-4118 124 23 satsuma satsuma NOUN american_scientific_journal-4118 124 24 coupled couple VERB american_scientific_journal-4118 124 25 kdv kdv NOUN american_scientific_journal-4118 124 26 system system NOUN american_scientific_journal-4118 124 27 with with ADP american_scientific_journal-4118 124 28 variable variable ADJ american_scientific_journal-4118 124 29 coefficients coefficient NOUN american_scientific_journal-4118 124 30 , , PUNCT american_scientific_journal-4118 124 31 inter inter PROPN american_scientific_journal-4118 124 32 . . PUNCT american_scientific_journal-4118 125 1 j. j. PROPN american_scientific_journal-4118 125 2 nonlinear nonlinear PROPN american_scientific_journal-4118 125 3 sci sci PROPN american_scientific_journal-4118 125 4 . . PUNCT american_scientific_journal-4118 126 1 7(2009 7(2009 NUM american_scientific_journal-4118 126 2 ): ): PUNCT american_scientific_journal-4118 126 3 29 29 NUM american_scientific_journal-4118 126 4 - - SYM american_scientific_journal-4118 126 5 38 38 NUM american_scientific_journal-4118 126 6 . . PUNCT american_scientific_journal-4118 127 1 [ [ X american_scientific_journal-4118 127 2 14 14 NUM american_scientific_journal-4118 127 3 ] ] PUNCT american_scientific_journal-4118 127 4 . . PUNCT american_scientific_journal-4118 128 1 vakhmenko vakhmenko PROPN american_scientific_journal-4118 128 2 v. v. CCONJ american_scientific_journal-4118 129 1 o. o. PROPN american_scientific_journal-4118 129 2 , , PUNCT american_scientific_journal-4118 129 3 parkers parker NOUN american_scientific_journal-4118 129 4 e. e. PROPN american_scientific_journal-4118 129 5 j. j. PROPN american_scientific_journal-4118 129 6 , , PUNCT american_scientific_journal-4118 129 7 the the DET american_scientific_journal-4118 129 8 calculation calculation NOUN american_scientific_journal-4118 129 9 of of ADP american_scientific_journal-4118 129 10 multi multi ADJ american_scientific_journal-4118 129 11 - - ADJ american_scientific_journal-4118 129 12 soliton soliton ADJ american_scientific_journal-4118 129 13 solutions solution NOUN american_scientific_journal-4118 129 14 of of ADP american_scientific_journal-4118 129 15 the the DET american_scientific_journal-4118 129 16 vakhnenko vakhnenko NOUN american_scientific_journal-4118 129 17 equation equation NOUN american_scientific_journal-4118 129 18 by by ADP american_scientific_journal-4118 129 19 the the DET american_scientific_journal-4118 129 20 inverse inverse NOUN american_scientific_journal-4118 129 21 scattering scattering NOUN american_scientific_journal-4118 129 22 method method NOUN american_scientific_journal-4118 129 23 . . PUNCT american_scientific_journal-4118 130 1 chaos chaos NOUN american_scientific_journal-4118 130 2 , , PUNCT american_scientific_journal-4118 130 3 solutions solution NOUN american_scientific_journal-4118 130 4 & & CCONJ american_scientific_journal-4118 130 5 fractals fractal NOUN american_scientific_journal-4118 130 6 . . PUNCT american_scientific_journal-4118 131 1 13(2003 13(2003 NUM american_scientific_journal-4118 131 2 ): ): PUNCT american_scientific_journal-4118 131 3 1819 1819 NUM american_scientific_journal-4118 131 4 - - SYM american_scientific_journal-4118 131 5 1826 1826 NUM american_scientific_journal-4118 131 6 . . PUNCT american_scientific_journal-4118 132 1 [ [ X american_scientific_journal-4118 132 2 15 15 NUM american_scientific_journal-4118 132 3 ] ] PUNCT american_scientific_journal-4118 132 4 . . PUNCT american_scientific_journal-4118 133 1 abdou abdou PROPN american_scientific_journal-4118 133 2 m. m. PROPN american_scientific_journal-4118 133 3 a. a. PROPN american_scientific_journal-4118 133 4 , , PUNCT american_scientific_journal-4118 133 5 soliman soliman PROPN american_scientific_journal-4118 133 6 a. a. PROPN american_scientific_journal-4118 133 7 a. a. PROPN american_scientific_journal-4118 133 8 , , PUNCT american_scientific_journal-4118 133 9 new new ADJ american_scientific_journal-4118 133 10 applications application NOUN american_scientific_journal-4118 133 11 of of ADP american_scientific_journal-4118 133 12 variational variational ADJ american_scientific_journal-4118 133 13 iteration iteration NOUN american_scientific_journal-4118 133 14 method method NOUN american_scientific_journal-4118 133 15 . . PUNCT american_scientific_journal-4118 134 1 physica physica PROPN american_scientific_journal-4118 134 2 d d PROPN american_scientific_journal-4118 134 3 , , PUNCT american_scientific_journal-4118 134 4 211 211 NUM american_scientific_journal-4118 134 5 ( ( PUNCT american_scientific_journal-4118 134 6 1–2 1–2 NUM american_scientific_journal-4118 134 7 ) ) PUNCT american_scientific_journal-4118 134 8 , , PUNCT american_scientific_journal-4118 134 9 2005 2005 NUM american_scientific_journal-4118 134 10 , , PUNCT american_scientific_journal-4118 134 11 1–8 1–8 NUM american_scientific_journal-4118 134 12 . . PUNCT american_scientific_journal-4118 135 1 [ [ X american_scientific_journal-4118 135 2 16 16 NUM american_scientific_journal-4118 135 3 ] ] PUNCT american_scientific_journal-4118 135 4 . . PUNCT american_scientific_journal-4118 136 1 bekir bekir PROPN american_scientific_journal-4118 136 2 a. a. PROPN american_scientific_journal-4118 136 3 and and CCONJ american_scientific_journal-4118 136 4 boz boz PROPN american_scientific_journal-4118 136 5 a. a. PROPN american_scientific_journal-4118 136 6 , , PUNCT american_scientific_journal-4118 136 7 exact exact ADJ american_scientific_journal-4118 136 8 solutions solution NOUN american_scientific_journal-4118 136 9 for for ADP american_scientific_journal-4118 136 10 nonlinear nonlinear ADJ american_scientific_journal-4118 136 11 evolution evolution NOUN american_scientific_journal-4118 136 12 equation equation NOUN american_scientific_journal-4118 136 13 using use VERB american_scientific_journal-4118 136 14 exp exp NOUN american_scientific_journal-4118 136 15 - - PUNCT american_scientific_journal-4118 136 16 function function NOUN american_scientific_journal-4118 136 17 method method NOUN american_scientific_journal-4118 136 18 , , PUNCT american_scientific_journal-4118 136 19 physics physics NOUN american_scientific_journal-4118 136 20 letters letter NOUN american_scientific_journal-4118 136 21 a a DET american_scientific_journal-4118 136 22 372(2008 372(2008 NOUN american_scientific_journal-4118 136 23 ) ) PUNCT american_scientific_journal-4118 136 24 , , PUNCT american_scientific_journal-4118 136 25 1619–1625 1619–1625 NUM american_scientific_journal-4118 136 26 . . PUNCT american_scientific_journal-4118 137 1 [ [ X american_scientific_journal-4118 137 2 17 17 NUM american_scientific_journal-4118 137 3 ] ] PUNCT american_scientific_journal-4118 137 4 . . PUNCT american_scientific_journal-4118 138 1 islam islam PROPN american_scientific_journal-4118 138 2 m. m. PROPN american_scientific_journal-4118 138 3 e. e. PROPN american_scientific_journal-4118 138 4 , , PUNCT american_scientific_journal-4118 138 5 khan khan PROPN american_scientific_journal-4118 138 6 k. k. PROPN american_scientific_journal-4118 138 7 , , PUNCT american_scientific_journal-4118 138 8 akbar akbar NOUN american_scientific_journal-4118 138 9 m. m. NOUN american_scientific_journal-4118 138 10 a. a. PROPN american_scientific_journal-4118 138 11 and and CCONJ american_scientific_journal-4118 138 12 islam islam PROPN american_scientific_journal-4118 138 13 r. r. PROPN american_scientific_journal-4118 138 14 , , PUNCT american_scientific_journal-4118 138 15 traveling travel VERB american_scientific_journal-4118 138 16 wave wave NOUN american_scientific_journal-4118 138 17 solutions solution NOUN american_scientific_journal-4118 138 18 of of ADP american_scientific_journal-4118 138 19 nonlinear nonlinear ADJ american_scientific_journal-4118 138 20 evolution evolution NOUN american_scientific_journal-4118 138 21 equation equation NOUN american_scientific_journal-4118 138 22 via via ADP american_scientific_journal-4118 138 23 enhanced enhanced ADJ american_scientific_journal-4118 138 24 ( ( PUNCT american_scientific_journal-4118 138 25 g'/g)-expansion g'/g)-expansion NOUN american_scientific_journal-4118 138 26 method method NOUN american_scientific_journal-4118 138 27 . . PUNCT american_scientific_journal-4118 139 1 ganit ganit PROPN american_scientific_journal-4118 139 2 j. j. PROPN american_scientific_journal-4118 139 3 bangladesh bangladesh PROPN american_scientific_journal-4118 139 4 math math PROPN american_scientific_journal-4118 139 5 . . PUNCT american_scientific_journal-4118 140 1 soc soc PROPN american_scientific_journal-4118 140 2 . . PUNCT american_scientific_journal-4118 140 3 , , PUNCT american_scientific_journal-4118 140 4 ( ( PUNCT american_scientific_journal-4118 140 5 issn issn PROPN american_scientific_journal-4118 140 6 16063694 16063694 NUM american_scientific_journal-4118 140 7 ) ) PUNCT american_scientific_journal-4118 140 8 vol vol NOUN american_scientific_journal-4118 140 9 . . PROPN american_scientific_journal-4118 141 1 33 33 NUM american_scientific_journal-4118 141 2 , , PUNCT american_scientific_journal-4118 141 3 2013 2013 NUM american_scientific_journal-4118 141 4 , , PUNCT american_scientific_journal-4118 141 5 83 83 NUM american_scientific_journal-4118 141 6 - - SYM american_scientific_journal-4118 141 7 92 92 NUM american_scientific_journal-4118 141 8 . . PUNCT american_scientific_journal-4118 142 1 [ [ X american_scientific_journal-4118 142 2 18 18 NUM american_scientific_journal-4118 142 3 ] ] PUNCT american_scientific_journal-4118 142 4 . . PUNCT american_scientific_journal-4118 143 1 jawad jawad PROPN american_scientific_journal-4118 143 2 a. a. PROPN american_scientific_journal-4118 143 3 j. j. PROPN american_scientific_journal-4118 143 4 m. m. PROPN american_scientific_journal-4118 143 5 , , PUNCT american_scientific_journal-4118 143 6 petkoviΒ΄c petkoviΒ΄c NOUN american_scientific_journal-4118 143 7 m. m. NOUN american_scientific_journal-4118 143 8 d. d. PROPN american_scientific_journal-4118 143 9 and and CCONJ american_scientific_journal-4118 143 10 biswas biswas PROPN american_scientific_journal-4118 143 11 a. a. PROPN american_scientific_journal-4118 143 12 , , PUNCT american_scientific_journal-4118 143 13 modified modify VERB american_scientific_journal-4118 143 14 simple simple ADJ american_scientific_journal-4118 143 15 equation equation NOUN american_scientific_journal-4118 143 16 method method NOUN american_scientific_journal-4118 143 17 for for ADP american_scientific_journal-4118 143 18 nonlinear nonlinear ADJ american_scientific_journal-4118 143 19 evolution evolution NOUN american_scientific_journal-4118 143 20 equations equation NOUN american_scientific_journal-4118 143 21 , , PUNCT american_scientific_journal-4118 143 22 app app PROPN american_scientific_journal-4118 143 23 . . PROPN american_scientific_journal-4118 143 24 math math PROPN american_scientific_journal-4118 143 25 . . PUNCT american_scientific_journal-4118 144 1 and and CCONJ american_scientific_journal-4118 144 2 compu compu PROPN american_scientific_journal-4118 144 3 . . PROPN american_scientific_journal-4118 144 4 , , PUNCT american_scientific_journal-4118 144 5 vol vol NOUN american_scientific_journal-4118 144 6 . . PROPN american_scientific_journal-4118 145 1 217 217 NUM american_scientific_journal-4118 145 2 , , PUNCT american_scientific_journal-4118 145 3 no no INTJ american_scientific_journal-4118 145 4 . . NOUN american_scientific_journal-4118 145 5 2 2 NUM american_scientific_journal-4118 145 6 , , PUNCT american_scientific_journal-4118 145 7 ( ( PUNCT american_scientific_journal-4118 145 8 2010 2010 NUM american_scientific_journal-4118 145 9 ) ) PUNCT american_scientific_journal-4118 145 10 , , PUNCT american_scientific_journal-4118 145 11 pp pp ADP american_scientific_journal-4118 145 12 . . PUNCT american_scientific_journal-4118 146 1 869–877 869–877 NUM american_scientific_journal-4118 146 2 . . PUNCT american_scientific_journal-4118 147 1 [ [ X american_scientific_journal-4118 147 2 19 19 NUM american_scientific_journal-4118 147 3 ] ] PUNCT american_scientific_journal-4118 147 4 . . PUNCT american_scientific_journal-4118 148 1 wang wang PROPN american_scientific_journal-4118 148 2 m. m. PROPN american_scientific_journal-4118 148 3 , , PUNCT american_scientific_journal-4118 148 4 li li PROPN american_scientific_journal-4118 148 5 x. x. PROPN american_scientific_journal-4118 148 6 , , PUNCT american_scientific_journal-4118 148 7 extended extend VERB american_scientific_journal-4118 148 8 f f NOUN american_scientific_journal-4118 148 9 - - PUNCT american_scientific_journal-4118 148 10 expansion expansion NOUN american_scientific_journal-4118 148 11 and and CCONJ american_scientific_journal-4118 148 12 periodic periodic ADJ american_scientific_journal-4118 148 13 wave wave NOUN american_scientific_journal-4118 148 14 solutions solution NOUN american_scientific_journal-4118 148 15 for for ADP american_scientific_journal-4118 148 16 the the DET american_scientific_journal-4118 148 17 generalized generalize VERB american_scientific_journal-4118 148 18 zakharov zakharov ADJ american_scientific_journal-4118 148 19 equations equation NOUN american_scientific_journal-4118 148 20 . . PUNCT american_scientific_journal-4118 149 1 phys phy NOUN american_scientific_journal-4118 149 2 . . PUNCT american_scientific_journal-4118 150 1 lett lett PROPN american_scientific_journal-4118 150 2 . . PUNCT american_scientific_journal-4118 151 1 a. a. PROPN american_scientific_journal-4118 151 2 343(2005 343(2005 NUM american_scientific_journal-4118 151 3 ): ): PUNCT american_scientific_journal-4118 151 4 48 48 NUM american_scientific_journal-4118 151 5 - - SYM american_scientific_journal-4118 151 6 54 54 NUM american_scientific_journal-4118 151 7 . . PUNCT american_scientific_journal-4118 152 1 [ [ X american_scientific_journal-4118 152 2 20 20 NUM american_scientific_journal-4118 152 3 ] ] PUNCT american_scientific_journal-4118 152 4 . . PUNCT american_scientific_journal-4118 153 1 wang wang PROPN american_scientific_journal-4118 153 2 m. m. PROPN american_scientific_journal-4118 153 3 , , PUNCT american_scientific_journal-4118 153 4 li li PROPN american_scientific_journal-4118 153 5 x. x. PROPN american_scientific_journal-4118 153 6 , , PUNCT american_scientific_journal-4118 153 7 applications application NOUN american_scientific_journal-4118 153 8 of of ADP american_scientific_journal-4118 153 9 f f NOUN american_scientific_journal-4118 153 10 - - PUNCT american_scientific_journal-4118 153 11 expansion expansion NOUN american_scientific_journal-4118 153 12 to to ADP american_scientific_journal-4118 153 13 periodic periodic ADJ american_scientific_journal-4118 153 14 wave wave NOUN american_scientific_journal-4118 153 15 solutions solution NOUN american_scientific_journal-4118 153 16 for for ADP american_scientific_journal-4118 153 17 a a DET american_scientific_journal-4118 153 18 new new ADJ american_scientific_journal-4118 153 19 hamiltonian hamiltonian ADJ american_scientific_journal-4118 153 20 amplitude amplitude NOUN american_scientific_journal-4118 153 21 equation equation NOUN american_scientific_journal-4118 153 22 . . PUNCT american_scientific_journal-4118 154 1 chaos chaos NOUN american_scientific_journal-4118 154 2 , , PUNCT american_scientific_journal-4118 154 3 solutions solution NOUN american_scientific_journal-4118 154 4 & & CCONJ american_scientific_journal-4118 154 5 fractals fractal NOUN american_scientific_journal-4118 154 6 . . PUNCT american_scientific_journal-4118 155 1 24(2005 24(2005 NUM american_scientific_journal-4118 155 2 ): ): PUNCT american_scientific_journal-4118 155 3 1257 1257 NUM american_scientific_journal-4118 155 4 - - SYM american_scientific_journal-4118 155 5 1268 1268 NUM american_scientific_journal-4118 155 6 . . PUNCT american_scientific_journal-4118 156 1 [ [ X american_scientific_journal-4118 156 2 21 21 NUM american_scientific_journal-4118 156 3 ] ] PUNCT american_scientific_journal-4118 156 4 . . PUNCT american_scientific_journal-4118 157 1 ben ben PROPN american_scientific_journal-4118 157 2 jing jing PROPN american_scientific_journal-4118 157 3 . . PUNCT american_scientific_journal-4118 158 1 a a DET american_scientific_journal-4118 158 2 new new ADJ american_scientific_journal-4118 158 3 bernoulli bernoulli PROPN american_scientific_journal-4118 158 4 sub sub X american_scientific_journal-4118 158 5 ode ode PROPN american_scientific_journal-4118 158 6 method method NOUN american_scientific_journal-4118 158 7 for for ADP american_scientific_journal-4118 158 8 constructing construct VERB american_scientific_journal-4118 158 9 travelling travel VERB american_scientific_journal-4118 158 10 wave wave NOUN american_scientific_journal-4118 158 11 solutions solution NOUN american_scientific_journal-4118 158 12 for for ADP american_scientific_journal-4118 158 13 two two NUM american_scientific_journal-4118 158 14 nonlinear nonlinear ADJ american_scientific_journal-4118 158 15 equations equation NOUN american_scientific_journal-4118 158 16 with with ADP american_scientific_journal-4118 158 17 any any DET american_scientific_journal-4118 158 18 order order NOUN american_scientific_journal-4118 158 19 . . PUNCT american_scientific_journal-4118 159 1 u.p.b u.p.b ADJ american_scientific_journal-4118 159 2 science science PROPN american_scientific_journal-4118 159 3 bulletin bulletin NOUN american_scientific_journal-4118 159 4 , , PUNCT american_scientific_journal-4118 159 5 series series NOUN american_scientific_journal-4118 159 6 a a NOUN american_scientific_journal-4118 159 7 , , PUNCT american_scientific_journal-4118 159 8 vol.73 vol.73 ADV american_scientific_journal-4118 159 9 , , PUNCT american_scientific_journal-4118 159 10 issue issue NOUN american_scientific_journal-4118 159 11 3 3 NUM american_scientific_journal-4118 159 12 , , PUNCT american_scientific_journal-4118 159 13 page page NOUN american_scientific_journal-4118 159 14 85 85 NUM american_scientific_journal-4118 159 15 - - SYM american_scientific_journal-4118 159 16 93 93 NUM american_scientific_journal-4118 159 17 , , PUNCT american_scientific_journal-4118 159 18 2011 2011 NUM american_scientific_journal-4118 159 19 . . PUNCT american_scientific_journal-4118 160 1 [ [ X american_scientific_journal-4118 160 2 22 22 NUM american_scientific_journal-4118 160 3 ] ] PUNCT american_scientific_journal-4118 160 4 . . PUNCT american_scientific_journal-4118 161 1 xu xu PROPN american_scientific_journal-4118 161 2 f. f. PROPN american_scientific_journal-4118 161 3 , , PUNCT american_scientific_journal-4118 161 4 and and CCONJ american_scientific_journal-4118 161 5 feng feng PROPN american_scientific_journal-4118 161 6 q. q. PROPN american_scientific_journal-4118 161 7 a. a. PROPN american_scientific_journal-4118 161 8 generalized generalize VERB american_scientific_journal-4118 161 9 sub sub ADJ american_scientific_journal-4118 161 10 - - ADJ american_scientific_journal-4118 161 11 ode ode ADJ american_scientific_journal-4118 161 12 method method NOUN american_scientific_journal-4118 161 13 and and CCONJ american_scientific_journal-4118 161 14 applications application NOUN american_scientific_journal-4118 161 15 for for ADP american_scientific_journal-4118 161 16 nonlinear nonlinear ADJ american_scientific_journal-4118 161 17 evolution evolution NOUN american_scientific_journal-4118 161 18 american american PROPN american_scientific_journal-4118 161 19 scientific scientific ADJ american_scientific_journal-4118 161 20 research research PROPN american_scientific_journal-4118 161 21 journal journal NOUN american_scientific_journal-4118 161 22 for for ADP american_scientific_journal-4118 161 23 engineering engineering NOUN american_scientific_journal-4118 161 24 , , PUNCT american_scientific_journal-4118 161 25 technology technology NOUN american_scientific_journal-4118 161 26 , , PUNCT american_scientific_journal-4118 161 27 and and CCONJ american_scientific_journal-4118 161 28 sciences science NOUN american_scientific_journal-4118 161 29 ( ( PUNCT american_scientific_journal-4118 161 30 asrjets asrjet NOUN american_scientific_journal-4118 161 31 ) ) PUNCT american_scientific_journal-4118 161 32 ( ( PUNCT american_scientific_journal-4118 161 33 2018 2018 NUM american_scientific_journal-4118 161 34 ) ) PUNCT american_scientific_journal-4118 161 35 volume volume NOUN american_scientific_journal-4118 161 36 44 44 NUM american_scientific_journal-4118 161 37 , , PUNCT american_scientific_journal-4118 161 38 no no DET american_scientific_journal-4118 161 39 1 1 NUM american_scientific_journal-4118 161 40 , , PUNCT american_scientific_journal-4118 161 41 pp pp ADV american_scientific_journal-4118 161 42 58 58 NUM american_scientific_journal-4118 161 43 - - SYM american_scientific_journal-4118 161 44 67 67 NUM american_scientific_journal-4118 161 45 67 67 NUM american_scientific_journal-4118 161 46 equation equation NOUN american_scientific_journal-4118 161 47 s. s. PROPN american_scientific_journal-4118 161 48 j. j. PROPN american_scientific_journal-4118 161 49 sci sci PROPN american_scientific_journal-4118 161 50 . . PUNCT american_scientific_journal-4118 162 1 res res PROPN american_scientific_journal-4118 162 2 . . PUNCT american_scientific_journal-4118 162 3 report report NOUN american_scientific_journal-4118 162 4 . . PUNCT american_scientific_journal-4118 163 1 2(2 2(2 NUM american_scientific_journal-4118 163 2 ): ): PUNCT american_scientific_journal-4118 163 3 571 571 NUM american_scientific_journal-4118 163 4 - - SYM american_scientific_journal-4118 163 5 581 581 NUM american_scientific_journal-4118 163 6 , , PUNCT american_scientific_journal-4118 163 7 2013 2013 NUM american_scientific_journal-4118 163 8 . . PUNCT american_scientific_journal-4118 164 1 [ [ X american_scientific_journal-4118 164 2 23 23 NUM american_scientific_journal-4118 164 3 ] ] PUNCT american_scientific_journal-4118 164 4 . . PUNCT american_scientific_journal-4118 165 1 mahmoud mahmoud PROPN american_scientific_journal-4118 165 2 a.e a.e PROPN american_scientific_journal-4118 165 3 . . PROPN american_scientific_journal-4118 165 4 abdelrahman abdelrahman PROPN american_scientific_journal-4118 165 5 . . PUNCT american_scientific_journal-4118 166 1 exact exact ADJ american_scientific_journal-4118 166 2 traveling travel VERB american_scientific_journal-4118 166 3 wave wave NOUN american_scientific_journal-4118 166 4 solutions solution NOUN american_scientific_journal-4118 166 5 for for ADP american_scientific_journal-4118 166 6 fitzhugh fitzhugh NOUN american_scientific_journal-4118 166 7 - - PUNCT american_scientific_journal-4118 166 8 nagumo(fn nagumo(fn NOUN american_scientific_journal-4118 166 9 ) ) PUNCT american_scientific_journal-4118 166 10 equation equation NOUN american_scientific_journal-4118 166 11 and and CCONJ american_scientific_journal-4118 166 12 modified modify VERB american_scientific_journal-4118 166 13 liouville liouville NOUN american_scientific_journal-4118 166 14 equation equation NOUN american_scientific_journal-4118 166 15 . . PUNCT american_scientific_journal-4118 167 1 international international ADJ american_scientific_journal-4118 167 2 journal journal PROPN american_scientific_journal-4118 167 3 of of ADP american_scientific_journal-4118 167 4 computer computer NOUN american_scientific_journal-4118 167 5 applications application NOUN american_scientific_journal-4118 167 6 ( ( PUNCT american_scientific_journal-4118 167 7 0975 0975 NUM american_scientific_journal-4118 167 8 8887 8887 NUM american_scientific_journal-4118 167 9 ) ) PUNCT american_scientific_journal-4118 167 10 , , PUNCT american_scientific_journal-4118 167 11 volume volume NOUN american_scientific_journal-4118 167 12 113 113 NUM american_scientific_journal-4118 167 13 no no NOUN american_scientific_journal-4118 167 14 . . PROPN american_scientific_journal-4118 168 1 3 3 NUM american_scientific_journal-4118 168 2 , , PUNCT american_scientific_journal-4118 168 3 march march PROPN american_scientific_journal-4118 168 4 2015 2015 NUM american_scientific_journal-4118 168 5 . . PUNCT american_scientific_journal-4118 169 1 [ [ X american_scientific_journal-4118 169 2 24 24 NUM american_scientific_journal-4118 169 3 ] ] PUNCT american_scientific_journal-4118 169 4 . . PUNCT american_scientific_journal-4118 170 1 salam salam PROPN american_scientific_journal-4118 170 2 m. m. PROPN american_scientific_journal-4118 170 3 a. a. PROPN american_scientific_journal-4118 170 4 , , PUNCT american_scientific_journal-4118 170 5 traveling traveling ADJ american_scientific_journal-4118 170 6 - - PUNCT american_scientific_journal-4118 170 7 wave wave NOUN american_scientific_journal-4118 170 8 solution solution NOUN american_scientific_journal-4118 170 9 of of ADP american_scientific_journal-4118 170 10 modified modify VERB american_scientific_journal-4118 170 11 liouville liouville NOUN american_scientific_journal-4118 170 12 equation equation NOUN american_scientific_journal-4118 170 13 by by ADP american_scientific_journal-4118 170 14 means mean NOUN american_scientific_journal-4118 170 15 of of ADP american_scientific_journal-4118 170 16 modified modify VERB american_scientific_journal-4118 170 17 simple simple ADJ american_scientific_journal-4118 170 18 equation equation NOUN american_scientific_journal-4118 170 19 method method NOUN american_scientific_journal-4118 170 20 , , PUNCT american_scientific_journal-4118 170 21 isrn isrn NOUN american_scientific_journal-4118 170 22 applied apply VERB american_scientific_journal-4118 170 23 mathematics mathematic NOUN american_scientific_journal-4118 170 24 , , PUNCT american_scientific_journal-4118 170 25 article article NOUN american_scientific_journal-4118 170 26 i i PROPN american_scientific_journal-4118 170 27 d d PROPN american_scientific_journal-4118 170 28 565247,4 565247,4 NUM american_scientific_journal-4118 170 29 pages page NOUN american_scientific_journal-4118 170 30 doi:10.5402/2012/565247 doi:10.5402/2012/565247 NOUN american_scientific_journal-4118 170 31 , , PUNCT american_scientific_journal-4118 170 32 2012 2012 NUM american_scientific_journal-4118 170 33 . . PUNCT american_scientific_journal-4118 171 1 [ [ X american_scientific_journal-4118 171 2 25 25 NUM american_scientific_journal-4118 171 3 ] ] PUNCT american_scientific_journal-4118 171 4 . . PUNCT american_scientific_journal-4118 172 1 wazwaz wazwaz PROPN american_scientific_journal-4118 172 2 a.m. a.m. PROPN american_scientific_journal-4118 172 3 a. a. PROPN american_scientific_journal-4118 172 4 sine sine PROPN american_scientific_journal-4118 172 5 - - PUNCT american_scientific_journal-4118 172 6 cosine cosine NOUN american_scientific_journal-4118 172 7 method method NOUN american_scientific_journal-4118 172 8 for for ADP american_scientific_journal-4118 172 9 handling handle VERB american_scientific_journal-4118 172 10 nonlinear nonlinear ADJ american_scientific_journal-4118 172 11 wave wave NOUN american_scientific_journal-4118 172 12 equations equation NOUN american_scientific_journal-4118 172 13 . . PUNCT american_scientific_journal-4118 173 1 math math NOUN american_scientific_journal-4118 173 2 . . PUNCT american_scientific_journal-4118 174 1 and and CCONJ american_scientific_journal-4118 174 2 comput comput NOUN american_scientific_journal-4118 174 3 . . PUNCT american_scientific_journal-4118 175 1 modelling modelling NOUN american_scientific_journal-4118 175 2 . . PUNCT american_scientific_journal-4118 176 1 40 40 NUM american_scientific_journal-4118 176 2 , , PUNCT american_scientific_journal-4118 176 3 499 499 NUM american_scientific_journal-4118 176 4 - - SYM american_scientific_journal-4118 176 5 508 508 NUM american_scientific_journal-4118 176 6 , , PUNCT american_scientific_journal-4118 176 7 2004 2004 NUM american_scientific_journal-4118 176 8 . . PUNCT