id sid tid token lemma pos ejpam-2219 1 1 european european PROPN ejpam-2219 1 2 journal journal PROPN ejpam-2219 1 3 of of ADP ejpam-2219 1 4 pure pure ADJ ejpam-2219 1 5 and and CCONJ ejpam-2219 1 6 applied apply VERB ejpam-2219 1 7 mathematics mathematic NOUN ejpam-2219 1 8 vol vol NOUN ejpam-2219 1 9 . . PROPN ejpam-2219 2 1 10 10 NUM ejpam-2219 2 2 , , PUNCT ejpam-2219 2 3 no no INTJ ejpam-2219 2 4 . . NOUN ejpam-2219 2 5 3 3 NUM ejpam-2219 2 6 , , PUNCT ejpam-2219 2 7 2017 2017 NUM ejpam-2219 2 8 , , PUNCT ejpam-2219 2 9 563 563 NUM ejpam-2219 2 10 - - SYM ejpam-2219 2 11 573 573 NUM ejpam-2219 2 12 issn issn PROPN ejpam-2219 2 13 1307 1307 NUM ejpam-2219 2 14 - - SYM ejpam-2219 2 15 5543 5543 NUM ejpam-2219 2 16 – – PUNCT ejpam-2219 2 17 www.ejpam.com www.ejpam.com X ejpam-2219 2 18 published publish VERB ejpam-2219 2 19 by by ADP ejpam-2219 2 20 new new PROPN ejpam-2219 2 21 york york PROPN ejpam-2219 2 22 business business PROPN ejpam-2219 2 23 global global ADJ ejpam-2219 2 24 canonical canonical ADJ ejpam-2219 2 25 reduction reduction NOUN ejpam-2219 2 26 of of ADP ejpam-2219 2 27 the the DET ejpam-2219 2 28 self self NOUN ejpam-2219 2 29 - - PUNCT ejpam-2219 2 30 dual dual ADJ ejpam-2219 2 31 yang yang PROPN ejpam-2219 2 32 mills mills PROPN ejpam-2219 2 33 equations equation NOUN ejpam-2219 2 34 to to ADP ejpam-2219 2 35 complex complex ADJ ejpam-2219 2 36 ginzburg ginzburg NOUN ejpam-2219 2 37 - - PUNCT ejpam-2219 2 38 landau landau NOUN ejpam-2219 2 39 equations equation NOUN ejpam-2219 2 40 and and CCONJ ejpam-2219 2 41 exact exact ADJ ejpam-2219 2 42 solutions solution NOUN ejpam-2219 2 43 a.r a.r PROPN ejpam-2219 2 44 . . PROPN ejpam-2219 2 45 shehata1,∗ shehata1,∗ PROPN ejpam-2219 2 46 , , PUNCT ejpam-2219 2 47 j.f.alzaidy j.f.alzaidy ADJ ejpam-2219 2 48 2 2 NUM ejpam-2219 2 49 1 1 NUM ejpam-2219 2 50 mathematics mathematics NOUN ejpam-2219 2 51 department department NOUN ejpam-2219 2 52 , , PUNCT ejpam-2219 2 53 faculty faculty NOUN ejpam-2219 2 54 of of ADP ejpam-2219 2 55 science science NOUN ejpam-2219 2 56 , , PUNCT ejpam-2219 2 57 minia minia NOUN ejpam-2219 2 58 university university NOUN ejpam-2219 2 59 , , PUNCT ejpam-2219 2 60 egypt egypt PROPN ejpam-2219 2 61 2 2 NUM ejpam-2219 2 62 mathematics mathematics PROPN ejpam-2219 2 63 department department NOUN ejpam-2219 2 64 , , PUNCT ejpam-2219 2 65 faculty faculty NOUN ejpam-2219 2 66 of of ADP ejpam-2219 2 67 science science NOUN ejpam-2219 2 68 , , PUNCT ejpam-2219 2 69 king king PROPN ejpam-2219 2 70 abdulaziz abdulaziz PROPN ejpam-2219 2 71 university university PROPN ejpam-2219 2 72 , , PUNCT ejpam-2219 2 73 saudi saudi PROPN ejpam-2219 2 74 arabia arabia PROPN ejpam-2219 2 75 abstract abstract NOUN ejpam-2219 2 76 . . PUNCT ejpam-2219 3 1 the the DET ejpam-2219 3 2 ( ( PUNCT ejpam-2219 3 3 constrained constrained ADJ ejpam-2219 3 4 ) ) PUNCT ejpam-2219 3 5 canonical canonical ADJ ejpam-2219 3 6 reduction reduction NOUN ejpam-2219 3 7 of of ADP ejpam-2219 3 8 four four NUM ejpam-2219 3 9 - - PUNCT ejpam-2219 3 10 dimensional dimensional ADJ ejpam-2219 3 11 self self NOUN ejpam-2219 3 12 - - PUNCT ejpam-2219 3 13 dual dual ADJ ejpam-2219 3 14 yang yang PROPN ejpam-2219 3 15 - - PUNCT ejpam-2219 3 16 mills mill NOUN ejpam-2219 3 17 ( ( PUNCT ejpam-2219 3 18 sdym sdym ADJ ejpam-2219 3 19 ) ) PUNCT ejpam-2219 3 20 theory theory NOUN ejpam-2219 3 21 to to ADP ejpam-2219 3 22 two two NUM ejpam-2219 3 23 - - PUNCT ejpam-2219 3 24 dimensional dimensional ADJ ejpam-2219 3 25 complex complex ADJ ejpam-2219 3 26 ginzburg ginzburg NOUN ejpam-2219 3 27 - - PUNCT ejpam-2219 3 28 landau landau NOUN ejpam-2219 3 29 equation equation NOUN ejpam-2219 3 30 are be AUX ejpam-2219 3 31 considered consider VERB ejpam-2219 3 32 . . PUNCT ejpam-2219 4 1 on on ADP ejpam-2219 4 2 the the DET ejpam-2219 4 3 other other ADJ ejpam-2219 4 4 hand hand NOUN ejpam-2219 4 5 , , PUNCT ejpam-2219 4 6 other other ADJ ejpam-2219 4 7 methods method NOUN ejpam-2219 4 8 and and CCONJ ejpam-2219 4 9 transformations transformation NOUN ejpam-2219 4 10 are be AUX ejpam-2219 4 11 developed develop VERB ejpam-2219 4 12 to to PART ejpam-2219 4 13 obtain obtain VERB ejpam-2219 4 14 exact exact ADJ ejpam-2219 4 15 solutions solution NOUN ejpam-2219 4 16 for for ADP ejpam-2219 4 17 the the DET ejpam-2219 4 18 original original ADJ ejpam-2219 4 19 two two NUM ejpam-2219 4 20 dimensional dimensional ADJ ejpam-2219 4 21 complex complex ADJ ejpam-2219 4 22 ginzburg ginzburg NOUN ejpam-2219 4 23 - - PUNCT ejpam-2219 4 24 landau landau NOUN ejpam-2219 4 25 equation equation NOUN ejpam-2219 4 26 . . PUNCT ejpam-2219 5 1 the the DET ejpam-2219 5 2 corresponding corresponding ADJ ejpam-2219 5 3 gauge gauge NOUN ejpam-2219 5 4 potential potential NOUN ejpam-2219 5 5 aµ aµ PROPN ejpam-2219 5 6 and and CCONJ ejpam-2219 5 7 the the DET ejpam-2219 5 8 gauge gauge ADJ ejpam-2219 5 9 field field NOUN ejpam-2219 5 10 strengths strength NOUN ejpam-2219 5 11 fµν fµν PRON ejpam-2219 5 12 are be AUX ejpam-2219 5 13 also also ADV ejpam-2219 5 14 obtained obtain VERB ejpam-2219 5 15 . . PUNCT ejpam-2219 6 1 for for ADP ejpam-2219 6 2 these these DET ejpam-2219 6 3 nonlinear nonlinear ADJ ejpam-2219 6 4 evolution evolution NOUN ejpam-2219 6 5 equations equation NOUN ejpam-2219 6 6 ( ( PUNCT ejpam-2219 6 7 nlees nlees PROPN ejpam-2219 6 8 ) ) PUNCT ejpam-2219 6 9 which which PRON ejpam-2219 6 10 describe describe VERB ejpam-2219 6 11 pseudo pseudo NOUN ejpam-2219 6 12 - - ADJ ejpam-2219 6 13 spherical spherical ADJ ejpam-2219 6 14 surfaces surface NOUN ejpam-2219 6 15 ( ( PUNCT ejpam-2219 6 16 pss pss PROPN ejpam-2219 6 17 ) ) PUNCT ejpam-2219 6 18 two two NUM ejpam-2219 6 19 new new ADJ ejpam-2219 6 20 exact exact ADJ ejpam-2219 6 21 solution solution NOUN ejpam-2219 6 22 classes class NOUN ejpam-2219 6 23 are be AUX ejpam-2219 6 24 generated generate VERB ejpam-2219 6 25 from from ADP ejpam-2219 6 26 known know VERB ejpam-2219 6 27 solutions solution NOUN ejpam-2219 6 28 by by ADP ejpam-2219 6 29 using use VERB ejpam-2219 6 30 the the DET ejpam-2219 6 31 bäcklund bäcklund NOUN ejpam-2219 6 32 transformations transformation NOUN ejpam-2219 6 33 with with ADP ejpam-2219 6 34 the the DET ejpam-2219 6 35 aid aid NOUN ejpam-2219 6 36 of of ADP ejpam-2219 6 37 mathematica mathematica PROPN ejpam-2219 6 38 , , PUNCT ejpam-2219 6 39 either either CCONJ ejpam-2219 6 40 the the DET ejpam-2219 6 41 seed seed NOUN ejpam-2219 6 42 solution solution NOUN ejpam-2219 6 43 is be AUX ejpam-2219 6 44 constant constant ADJ ejpam-2219 6 45 or or CCONJ ejpam-2219 6 46 a a DET ejpam-2219 6 47 traveling travel VERB ejpam-2219 6 48 wave wave NOUN ejpam-2219 6 49 . . PUNCT ejpam-2219 7 1 2010 2010 NUM ejpam-2219 7 2 mathematics mathematic NOUN ejpam-2219 7 3 subject subject NOUN ejpam-2219 7 4 classifications classification NOUN ejpam-2219 7 5 : : PUNCT ejpam-2219 7 6 35 35 NUM ejpam-2219 7 7 , , PUNCT ejpam-2219 7 8 53c 53c NOUN ejpam-2219 7 9 , , PUNCT ejpam-2219 7 10 58j 58j NUM ejpam-2219 7 11 , , PUNCT ejpam-2219 7 12 58z05 58z05 NUM ejpam-2219 7 13 key key ADJ ejpam-2219 7 14 words word NOUN ejpam-2219 7 15 and and CCONJ ejpam-2219 7 16 phrases phrase NOUN ejpam-2219 7 17 : : PUNCT ejpam-2219 7 18 sdym sdym ADJ ejpam-2219 7 19 , , PUNCT ejpam-2219 7 20 complex complex ADJ ejpam-2219 7 21 ginzburg ginzburg NOUN ejpam-2219 7 22 - - PUNCT ejpam-2219 7 23 landau landau NOUN ejpam-2219 7 24 equation equation NOUN ejpam-2219 7 25 , , PUNCT ejpam-2219 7 26 bäcklund bäcklund NOUN ejpam-2219 7 27 transformations transformation NOUN ejpam-2219 7 28 1 1 NUM ejpam-2219 7 29 . . PUNCT ejpam-2219 7 30 introduction introduction NOUN ejpam-2219 7 31 the the DET ejpam-2219 7 32 self self NOUN ejpam-2219 7 33 - - PUNCT ejpam-2219 7 34 dual dual ADJ ejpam-2219 7 35 yang yang PROPN ejpam-2219 7 36 - - PUNCT ejpam-2219 7 37 mills mill NOUN ejpam-2219 7 38 ( ( PUNCT ejpam-2219 7 39 sdym sdym ADJ ejpam-2219 7 40 ) ) PUNCT ejpam-2219 7 41 equations equation NOUN ejpam-2219 7 42 ( ( PUNCT ejpam-2219 7 43 a a DET ejpam-2219 7 44 system system NOUN ejpam-2219 7 45 of of ADP ejpam-2219 7 46 equations equation NOUN ejpam-2219 7 47 for for ADP ejpam-2219 7 48 lie lie NOUN ejpam-2219 7 49 algebravalued algebravalue VERB ejpam-2219 7 50 functions function NOUN ejpam-2219 7 51 of of ADP ejpam-2219 7 52 c4 c4 NOUN ejpam-2219 7 53 ) ) PUNCT ejpam-2219 7 54 play play VERB ejpam-2219 7 55 a a DET ejpam-2219 7 56 central central ADJ ejpam-2219 7 57 role role NOUN ejpam-2219 7 58 in in ADP ejpam-2219 7 59 the the DET ejpam-2219 7 60 field field NOUN ejpam-2219 7 61 of of ADP ejpam-2219 7 62 integrable integrable ADJ ejpam-2219 7 63 systems system NOUN ejpam-2219 7 64 and and CCONJ ejpam-2219 7 65 also also ADV ejpam-2219 7 66 play play VERB ejpam-2219 7 67 a a DET ejpam-2219 7 68 fundamental fundamental ADJ ejpam-2219 7 69 role role NOUN ejpam-2219 7 70 in in ADP ejpam-2219 7 71 several several ADJ ejpam-2219 7 72 other other ADJ ejpam-2219 7 73 areas area NOUN ejpam-2219 7 74 of of ADP ejpam-2219 7 75 mathematics mathematic NOUN ejpam-2219 7 76 and and CCONJ ejpam-2219 7 77 physics physics NOUN ejpam-2219 8 1 [ [ X ejpam-2219 8 2 17 17 NUM ejpam-2219 8 3 , , PUNCT ejpam-2219 8 4 14 14 NUM ejpam-2219 8 5 ] ] PUNCT ejpam-2219 8 6 . . PUNCT ejpam-2219 9 1 it it PRON ejpam-2219 9 2 arises arise VERB ejpam-2219 9 3 in in ADP ejpam-2219 9 4 relativity relativity NOUN ejpam-2219 9 5 [ [ X ejpam-2219 9 6 22 22 NUM ejpam-2219 9 7 , , PUNCT ejpam-2219 9 8 13 13 NUM ejpam-2219 9 9 ] ] PUNCT ejpam-2219 9 10 and and CCONJ ejpam-2219 9 11 in in ADP ejpam-2219 9 12 field field NOUN ejpam-2219 9 13 theory theory NOUN ejpam-2219 9 14 [ [ X ejpam-2219 9 15 6 6 NUM ejpam-2219 9 16 ] ] PUNCT ejpam-2219 9 17 . . PUNCT ejpam-2219 10 1 the the DET ejpam-2219 10 2 sdym sdym ADJ ejpam-2219 10 3 equations equation NOUN ejpam-2219 10 4 describe describe VERB ejpam-2219 10 5 a a DET ejpam-2219 10 6 connection connection NOUN ejpam-2219 10 7 for for ADP ejpam-2219 10 8 a a DET ejpam-2219 10 9 bundle bundle NOUN ejpam-2219 10 10 over over ADP ejpam-2219 10 11 the the DET ejpam-2219 10 12 grassmannian grassmannian NOUN ejpam-2219 10 13 of of ADP ejpam-2219 10 14 two two NUM ejpam-2219 10 15 - - PUNCT ejpam-2219 10 16 dimensional dimensional ADJ ejpam-2219 10 17 subspaces subspace NOUN ejpam-2219 10 18 of of ADP ejpam-2219 10 19 the the DET ejpam-2219 10 20 twistor twistor NOUN ejpam-2219 10 21 space space NOUN ejpam-2219 10 22 . . PUNCT ejpam-2219 11 1 integrability integrability NOUN ejpam-2219 11 2 for for ADP ejpam-2219 11 3 a a DET ejpam-2219 11 4 sdym sdym ADJ ejpam-2219 11 5 connection connection NOUN ejpam-2219 11 6 means mean VERB ejpam-2219 11 7 that that SCONJ ejpam-2219 11 8 its its PRON ejpam-2219 11 9 curvature curvature NOUN ejpam-2219 11 10 vanishes vanish VERB ejpam-2219 11 11 on on ADP ejpam-2219 11 12 certain certain ADJ ejpam-2219 11 13 two two NUM ejpam-2219 11 14 - - PUNCT ejpam-2219 11 15 planes plane NOUN ejpam-2219 11 16 in in ADP ejpam-2219 11 17 the the DET ejpam-2219 11 18 tangent tangent ADJ ejpam-2219 11 19 space space NOUN ejpam-2219 11 20 of of ADP ejpam-2219 11 21 the the DET ejpam-2219 11 22 grassmannian grassmannian ADJ ejpam-2219 11 23 . . PUNCT ejpam-2219 12 1 as as SCONJ ejpam-2219 12 2 shown show VERB ejpam-2219 12 3 in in ADP ejpam-2219 12 4 [ [ X ejpam-2219 12 5 18 18 NUM ejpam-2219 12 6 , , PUNCT ejpam-2219 12 7 21 21 NUM ejpam-2219 12 8 ] ] PUNCT ejpam-2219 12 9 . . PUNCT ejpam-2219 13 1 this this PRON ejpam-2219 13 2 allows allow VERB ejpam-2219 13 3 one one PRON ejpam-2219 13 4 to to PART ejpam-2219 13 5 characterize characterize VERB ejpam-2219 13 6 sdym sdym ADJ ejpam-2219 13 7 connections connection NOUN ejpam-2219 13 8 in in ADP ejpam-2219 13 9 terms term NOUN ejpam-2219 13 10 of of ADP ejpam-2219 13 11 the the DET ejpam-2219 13 12 splitting splitting NOUN ejpam-2219 13 13 problem problem NOUN ejpam-2219 13 14 for for ADP ejpam-2219 13 15 a a DET ejpam-2219 13 16 transition transition NOUN ejpam-2219 13 17 function function NOUN ejpam-2219 13 18 in in ADP ejpam-2219 13 19 a a DET ejpam-2219 13 20 holomorphic holomorphic ADJ ejpam-2219 13 21 bundle bundle NOUN ejpam-2219 13 22 over over ADP ejpam-2219 13 23 the the DET ejpam-2219 13 24 riemann riemann PROPN ejpam-2219 13 25 sphere sphere NOUN ejpam-2219 13 26 , , PUNCT ejpam-2219 13 27 i.e. i.e. X ejpam-2219 13 28 the the DET ejpam-2219 13 29 trivialization trivialization NOUN ejpam-2219 13 30 of of ADP ejpam-2219 13 31 the the DET ejpam-2219 13 32 bundle bundle NOUN ejpam-2219 13 33 [ [ X ejpam-2219 13 34 15 15 NUM ejpam-2219 13 35 , , PUNCT ejpam-2219 13 36 16 16 NUM ejpam-2219 13 37 ] ] PUNCT ejpam-2219 13 38 . . PUNCT ejpam-2219 14 1 ∗corresponding ∗corresponde VERB ejpam-2219 14 2 author author NOUN ejpam-2219 14 3 . . PUNCT ejpam-2219 15 1 email email NOUN ejpam-2219 15 2 addresses address NOUN ejpam-2219 15 3 : : PUNCT ejpam-2219 15 4 shehata1433@yahoo.com shehata1433@yahoo.com X ejpam-2219 16 1 ( ( PUNCT ejpam-2219 16 2 a.r a.r PROPN ejpam-2219 16 3 . . PROPN ejpam-2219 16 4 shehata shehata PROPN ejpam-2219 16 5 ) ) PUNCT ejpam-2219 16 6 , , PUNCT ejpam-2219 16 7 j-f-h-z@hotmail.com j-f-h-z@hotmail.com X ejpam-2219 16 8 ( ( PUNCT ejpam-2219 16 9 j.f.alzaidy j.f.alzaidy ADJ ejpam-2219 16 10 ) ) PUNCT ejpam-2219 16 11 http://www.ejpam.com http://www.ejpam.com X ejpam-2219 17 1 563 563 NUM ejpam-2219 17 2 c c X ejpam-2219 17 3 © © PROPN ejpam-2219 17 4 2017 2017 NUM ejpam-2219 17 5 ejpam ejpam NOUN ejpam-2219 17 6 all all DET ejpam-2219 17 7 rights right NOUN ejpam-2219 17 8 reserved reserve VERB ejpam-2219 17 9 . . PUNCT ejpam-2219 18 1 a.r a.r PROPN ejpam-2219 18 2 . . PROPN ejpam-2219 18 3 shehata shehata PROPN ejpam-2219 18 4 , , PUNCT ejpam-2219 18 5 j.f.alzaidy j.f.alzaidy ADJ ejpam-2219 18 6 / / SYM ejpam-2219 18 7 eur eur PROPN ejpam-2219 18 8 . . PUNCT ejpam-2219 19 1 j. j. PROPN ejpam-2219 19 2 pure pure PROPN ejpam-2219 19 3 appl appl PROPN ejpam-2219 19 4 . . PROPN ejpam-2219 19 5 math math PROPN ejpam-2219 19 6 , , PUNCT ejpam-2219 19 7 10 10 NUM ejpam-2219 19 8 ( ( PUNCT ejpam-2219 19 9 3 3 NUM ejpam-2219 19 10 ) ) PUNCT ejpam-2219 19 11 ( ( PUNCT ejpam-2219 19 12 2017 2017 NUM ejpam-2219 19 13 ) ) PUNCT ejpam-2219 19 14 , , PUNCT ejpam-2219 19 15 563 563 NUM ejpam-2219 19 16 - - SYM ejpam-2219 19 17 573 573 NUM ejpam-2219 19 18 564 564 NUM ejpam-2219 19 19 the the DET ejpam-2219 19 20 theory theory NOUN ejpam-2219 19 21 of of ADP ejpam-2219 19 22 integrable integrable ADJ ejpam-2219 19 23 systems system NOUN ejpam-2219 19 24 has have AUX ejpam-2219 19 25 been be AUX ejpam-2219 19 26 an an DET ejpam-2219 19 27 active active ADJ ejpam-2219 19 28 area area NOUN ejpam-2219 19 29 of of ADP ejpam-2219 19 30 mathematics mathematic NOUN ejpam-2219 19 31 for for ADP ejpam-2219 19 32 the the DET ejpam-2219 19 33 past past ADJ ejpam-2219 19 34 thirty thirty NUM ejpam-2219 19 35 years year NOUN ejpam-2219 19 36 . . PUNCT ejpam-2219 20 1 different different ADJ ejpam-2219 20 2 aspects aspect NOUN ejpam-2219 20 3 of of ADP ejpam-2219 20 4 the the DET ejpam-2219 20 5 subject subject NOUN ejpam-2219 20 6 have have VERB ejpam-2219 20 7 fundamental fundamental ADJ ejpam-2219 20 8 relations relation NOUN ejpam-2219 20 9 with with ADP ejpam-2219 20 10 mechanics mechanic NOUN ejpam-2219 20 11 and and CCONJ ejpam-2219 20 12 dynamics dynamic NOUN ejpam-2219 20 13 , , PUNCT ejpam-2219 20 14 applied apply VERB ejpam-2219 20 15 mathematics mathematic NOUN ejpam-2219 20 16 , , PUNCT ejpam-2219 20 17 algebraic algebraic ADJ ejpam-2219 20 18 structures structure NOUN ejpam-2219 20 19 , , PUNCT ejpam-2219 20 20 theoretical theoretical ADJ ejpam-2219 20 21 physics physics NOUN ejpam-2219 20 22 , , PUNCT ejpam-2219 20 23 analysis analysis NOUN ejpam-2219 20 24 including include VERB ejpam-2219 20 25 spectral spectral ADJ ejpam-2219 20 26 theory theory NOUN ejpam-2219 20 27 and and CCONJ ejpam-2219 20 28 geometry geometry NOUN ejpam-2219 20 29 . . PUNCT ejpam-2219 21 1 in in ADP ejpam-2219 21 2 recent recent ADJ ejpam-2219 21 3 decades decade NOUN ejpam-2219 21 4 , , PUNCT ejpam-2219 21 5 a a DET ejpam-2219 21 6 class class NOUN ejpam-2219 21 7 of of ADP ejpam-2219 21 8 transformations transformation NOUN ejpam-2219 21 9 having have VERB ejpam-2219 21 10 their their PRON ejpam-2219 21 11 origin origin NOUN ejpam-2219 21 12 in in ADP ejpam-2219 21 13 the the DET ejpam-2219 21 14 work work NOUN ejpam-2219 21 15 by by ADP ejpam-2219 21 16 bäcklund bäcklund NOUN ejpam-2219 21 17 in in ADP ejpam-2219 21 18 the the DET ejpam-2219 21 19 late late ADJ ejpam-2219 21 20 nineteenth nineteenth ADJ ejpam-2219 21 21 century century NOUN ejpam-2219 21 22 has have AUX ejpam-2219 21 23 provided provide VERB ejpam-2219 21 24 a a DET ejpam-2219 21 25 basis basis NOUN ejpam-2219 21 26 for for ADP ejpam-2219 21 27 remarkable remarkable ADJ ejpam-2219 21 28 advances advance NOUN ejpam-2219 21 29 in in ADP ejpam-2219 21 30 the the DET ejpam-2219 21 31 study study NOUN ejpam-2219 21 32 of of ADP ejpam-2219 21 33 nonlinear nonlinear ADJ ejpam-2219 21 34 partial partial ADJ ejpam-2219 21 35 differential differential NOUN ejpam-2219 21 36 equations equation NOUN ejpam-2219 21 37 ( ( PUNCT ejpam-2219 21 38 nlpdes)[17 nlpdes)[17 ADJ ejpam-2219 21 39 , , PUNCT ejpam-2219 21 40 14 14 NUM ejpam-2219 21 41 , , PUNCT ejpam-2219 21 42 22 22 NUM ejpam-2219 21 43 , , PUNCT ejpam-2219 21 44 13 13 NUM ejpam-2219 21 45 , , PUNCT ejpam-2219 21 46 6 6 NUM ejpam-2219 21 47 , , PUNCT ejpam-2219 21 48 18 18 NUM ejpam-2219 21 49 , , PUNCT ejpam-2219 21 50 21 21 NUM ejpam-2219 21 51 , , PUNCT ejpam-2219 21 52 15 15 NUM ejpam-2219 21 53 , , PUNCT ejpam-2219 21 54 16 16 NUM ejpam-2219 21 55 , , PUNCT ejpam-2219 21 56 12 12 NUM ejpam-2219 21 57 , , PUNCT ejpam-2219 21 58 10].the 10].the DET ejpam-2219 21 59 importance importance NOUN ejpam-2219 21 60 of of ADP ejpam-2219 21 61 bäcklund bäcklund NOUN ejpam-2219 21 62 transformations transformation NOUN ejpam-2219 21 63 ( ( PUNCT ejpam-2219 21 64 bts bt NOUN ejpam-2219 21 65 ) ) PUNCT ejpam-2219 21 66 and and CCONJ ejpam-2219 21 67 their their PRON ejpam-2219 21 68 generalizations generalization NOUN ejpam-2219 21 69 is be AUX ejpam-2219 21 70 basically basically ADV ejpam-2219 21 71 twofold twofold ADV ejpam-2219 21 72 . . PUNCT ejpam-2219 22 1 thus thus ADV ejpam-2219 22 2 , , PUNCT ejpam-2219 22 3 on on ADP ejpam-2219 22 4 one one NUM ejpam-2219 22 5 hand hand NOUN ejpam-2219 22 6 , , PUNCT ejpam-2219 22 7 invariance invariance NOUN ejpam-2219 22 8 under under ADP ejpam-2219 22 9 a a DET ejpam-2219 22 10 bt bt NOUN ejpam-2219 22 11 may may AUX ejpam-2219 22 12 be be AUX ejpam-2219 22 13 used use VERB ejpam-2219 22 14 to to PART ejpam-2219 22 15 generate generate VERB ejpam-2219 22 16 an an DET ejpam-2219 22 17 infinite infinite ADJ ejpam-2219 22 18 sequence sequence NOUN ejpam-2219 22 19 of of ADP ejpam-2219 22 20 solutions solution NOUN ejpam-2219 22 21 for for ADP ejpam-2219 22 22 certain certain ADJ ejpam-2219 22 23 nlpdes nlpde NOUN ejpam-2219 22 24 by by ADP ejpam-2219 22 25 purely purely ADV ejpam-2219 22 26 algebraic algebraic ADJ ejpam-2219 22 27 superposition superposition NOUN ejpam-2219 22 28 principles principle NOUN ejpam-2219 22 29 . . PUNCT ejpam-2219 23 1 on on ADP ejpam-2219 23 2 the the DET ejpam-2219 23 3 other other ADJ ejpam-2219 23 4 hand hand NOUN ejpam-2219 23 5 , , PUNCT ejpam-2219 23 6 bts bt NOUN ejpam-2219 23 7 may may AUX ejpam-2219 23 8 also also ADV ejpam-2219 23 9 be be AUX ejpam-2219 23 10 used use VERB ejpam-2219 23 11 to to PART ejpam-2219 23 12 link link VERB ejpam-2219 23 13 certain certain ADJ ejpam-2219 23 14 nlpdes[9 nlpdes[9 NOUN ejpam-2219 23 15 , , PUNCT ejpam-2219 23 16 24 24 NUM ejpam-2219 23 17 , , PUNCT ejpam-2219 23 18 25 25 NUM ejpam-2219 23 19 , , PUNCT ejpam-2219 23 20 19 19 NUM ejpam-2219 23 21 , , PUNCT ejpam-2219 23 22 14 14 NUM ejpam-2219 23 23 , , PUNCT ejpam-2219 23 24 28 28 NUM ejpam-2219 23 25 , , PUNCT ejpam-2219 23 26 11 11 NUM ejpam-2219 23 27 , , PUNCT ejpam-2219 23 28 7 7 NUM ejpam-2219 23 29 ] ] PUNCT ejpam-2219 23 30 ( ( PUNCT ejpam-2219 23 31 particularly particularly ADV ejpam-2219 23 32 nlees nlee VERB ejpam-2219 23 33 modelling model VERB ejpam-2219 23 34 nonlinear nonlinear ADJ ejpam-2219 23 35 waves wave NOUN ejpam-2219 23 36 ) ) PUNCT ejpam-2219 23 37 to to ADP ejpam-2219 23 38 canonical canonical ADJ ejpam-2219 23 39 forms form NOUN ejpam-2219 23 40 whose whose DET ejpam-2219 23 41 properties property NOUN ejpam-2219 23 42 are be AUX ejpam-2219 23 43 well well ADV ejpam-2219 23 44 known known ADJ ejpam-2219 23 45 [ [ X ejpam-2219 23 46 8 8 NUM ejpam-2219 23 47 , , PUNCT ejpam-2219 23 48 20 20 NUM ejpam-2219 23 49 , , PUNCT ejpam-2219 23 50 1 1 NUM ejpam-2219 23 51 ] ] PUNCT ejpam-2219 23 52 . . PUNCT ejpam-2219 24 1 nonlinear nonlinear ADJ ejpam-2219 24 2 wave wave NOUN ejpam-2219 24 3 phenomena phenomenon NOUN ejpam-2219 24 4 have have AUX ejpam-2219 24 5 attracted attract VERB ejpam-2219 24 6 the the DET ejpam-2219 24 7 attention attention NOUN ejpam-2219 24 8 of of ADP ejpam-2219 24 9 physicists physicist NOUN ejpam-2219 24 10 for for ADP ejpam-2219 24 11 a a DET ejpam-2219 24 12 long long ADJ ejpam-2219 24 13 time time NOUN ejpam-2219 24 14 . . PUNCT ejpam-2219 25 1 investigation investigation NOUN ejpam-2219 25 2 of of ADP ejpam-2219 25 3 a a DET ejpam-2219 25 4 certain certain ADJ ejpam-2219 25 5 kind kind NOUN ejpam-2219 25 6 of of ADP ejpam-2219 25 7 nlpdes nlpde NOUN ejpam-2219 25 8 has have AUX ejpam-2219 25 9 made make VERB ejpam-2219 25 10 great great ADJ ejpam-2219 25 11 progress progress NOUN ejpam-2219 25 12 in in ADP ejpam-2219 25 13 the the DET ejpam-2219 25 14 last last ADJ ejpam-2219 25 15 decades decade NOUN ejpam-2219 25 16 . . PUNCT ejpam-2219 26 1 these these DET ejpam-2219 26 2 equations equation NOUN ejpam-2219 26 3 have have VERB ejpam-2219 26 4 a a DET ejpam-2219 26 5 wide wide ADJ ejpam-2219 26 6 range range NOUN ejpam-2219 26 7 of of ADP ejpam-2219 26 8 physical physical ADJ ejpam-2219 26 9 applications application NOUN ejpam-2219 26 10 and and CCONJ ejpam-2219 26 11 share share VERB ejpam-2219 26 12 several several ADJ ejpam-2219 26 13 remarkable remarkable ADJ ejpam-2219 26 14 properties property NOUN ejpam-2219 26 15 [ [ X ejpam-2219 26 16 3 3 NUM ejpam-2219 26 17 , , PUNCT ejpam-2219 26 18 2 2 NUM ejpam-2219 26 19 , , PUNCT ejpam-2219 26 20 4 4 NUM ejpam-2219 26 21 , , PUNCT ejpam-2219 26 22 5 5 NUM ejpam-2219 26 23 ] ] NUM ejpam-2219 26 24 : : PUNCT ejpam-2219 26 25 ( ( PUNCT ejpam-2219 26 26 i i NOUN ejpam-2219 26 27 ) ) PUNCT ejpam-2219 26 28 the the DET ejpam-2219 26 29 initial initial ADJ ejpam-2219 26 30 value value NOUN ejpam-2219 26 31 problem problem NOUN ejpam-2219 26 32 can can AUX ejpam-2219 26 33 be be AUX ejpam-2219 26 34 solved solve VERB ejpam-2219 26 35 exactly exactly ADV ejpam-2219 26 36 in in ADP ejpam-2219 26 37 terms term NOUN ejpam-2219 26 38 of of ADP ejpam-2219 26 39 linear linear ADJ ejpam-2219 26 40 procedures procedure NOUN ejpam-2219 26 41 , , PUNCT ejpam-2219 26 42 the the DET ejpam-2219 26 43 so so ADV ejpam-2219 26 44 - - PUNCT ejpam-2219 26 45 called call VERB ejpam-2219 26 46 ” " PUNCT ejpam-2219 26 47 inverse inverse NOUN ejpam-2219 26 48 scattering scattering NOUN ejpam-2219 26 49 method method NOUN ejpam-2219 26 50 ( ( PUNCT ejpam-2219 26 51 ism ism NOUN ejpam-2219 26 52 ) ) PUNCT ejpam-2219 26 53 ” " PUNCT ejpam-2219 26 54 ; ; PUNCT ejpam-2219 26 55 ( ( PUNCT ejpam-2219 26 56 ii ii NOUN ejpam-2219 26 57 ) ) PUNCT ejpam-2219 26 58 they they PRON ejpam-2219 26 59 have have VERB ejpam-2219 26 60 an an DET ejpam-2219 26 61 infinite infinite ADJ ejpam-2219 26 62 number number NOUN ejpam-2219 26 63 of of ADP ejpam-2219 26 64 ” " PUNCT ejpam-2219 26 65 conservation conservation NOUN ejpam-2219 26 66 laws law NOUN ejpam-2219 26 67 ” " PUNCT ejpam-2219 26 68 ; ; PUNCT ejpam-2219 26 69 ( ( PUNCT ejpam-2219 26 70 iii iii X ejpam-2219 26 71 ) ) PUNCT ejpam-2219 26 72 they they PRON ejpam-2219 26 73 have have VERB ejpam-2219 26 74 ” " PUNCT ejpam-2219 26 75 bts bt NOUN ejpam-2219 26 76 ” " PUNCT ejpam-2219 26 77 ; ; PUNCT ejpam-2219 26 78 ( ( PUNCT ejpam-2219 26 79 iv iv X ejpam-2219 26 80 ) ) PUNCT ejpam-2219 26 81 they they PRON ejpam-2219 26 82 describe describe VERB ejpam-2219 26 83 pseudo pseudo NOUN ejpam-2219 26 84 - - ADJ ejpam-2219 26 85 spherical spherical ADJ ejpam-2219 26 86 surfaces surface NOUN ejpam-2219 26 87 ( ( PUNCT ejpam-2219 26 88 pss pss PROPN ejpam-2219 26 89 ) ) PUNCT ejpam-2219 26 90 , , PUNCT ejpam-2219 26 91 and and CCONJ ejpam-2219 26 92 hence hence ADV ejpam-2219 26 93 one one NUM ejpam-2219 26 94 may may AUX ejpam-2219 26 95 interpret interpret VERB ejpam-2219 26 96 the the DET ejpam-2219 26 97 other other ADJ ejpam-2219 26 98 properties property NOUN ejpam-2219 26 99 ( ( PUNCT ejpam-2219 26 100 i i PRON ejpam-2219 26 101 -iii -iii VERB ejpam-2219 26 102 ) ) PUNCT ejpam-2219 26 103 from from ADP ejpam-2219 26 104 a a DET ejpam-2219 26 105 geometrical geometrical ADJ ejpam-2219 26 106 point point NOUN ejpam-2219 26 107 of of ADP ejpam-2219 26 108 view view NOUN ejpam-2219 26 109 ; ; PUNCT ejpam-2219 26 110 ( ( PUNCT ejpam-2219 26 111 v v X ejpam-2219 26 112 ) ) PUNCT ejpam-2219 26 113 they they PRON ejpam-2219 26 114 are be AUX ejpam-2219 26 115 completely completely ADV ejpam-2219 26 116 integrable integrable ADJ ejpam-2219 26 117 [ [ X ejpam-2219 26 118 22 22 NUM ejpam-2219 26 119 , , PUNCT ejpam-2219 26 120 3 3 NUM ejpam-2219 26 121 , , PUNCT ejpam-2219 26 122 4 4 NUM ejpam-2219 26 123 ] ] PUNCT ejpam-2219 26 124 . . PUNCT ejpam-2219 27 1 non non ADJ ejpam-2219 27 2 - - ADJ ejpam-2219 27 3 abelian abelian ADJ ejpam-2219 27 4 gauge gauge NOUN ejpam-2219 27 5 theories theory NOUN ejpam-2219 27 6 first first ADV ejpam-2219 27 7 appeared appear VERB ejpam-2219 27 8 in in ADP ejpam-2219 27 9 the the DET ejpam-2219 27 10 seminal seminal ADJ ejpam-2219 27 11 work work NOUN ejpam-2219 27 12 of of ADP ejpam-2219 27 13 yang yang PROPN ejpam-2219 27 14 and and CCONJ ejpam-2219 27 15 mills mill NOUN ejpam-2219 27 16 [ [ X ejpam-2219 27 17 29 29 NUM ejpam-2219 27 18 ] ] PUNCT ejpam-2219 27 19 as as ADP ejpam-2219 27 20 a a DET ejpam-2219 27 21 non non ADJ ejpam-2219 27 22 - - ADJ ejpam-2219 27 23 abelian abelian ADJ ejpam-2219 27 24 generalization generalization NOUN ejpam-2219 27 25 of of ADP ejpam-2219 27 26 maxwell maxwell PROPN ejpam-2219 27 27 ’s ’s PART ejpam-2219 27 28 equations equation NOUN ejpam-2219 27 29 . . PUNCT ejpam-2219 28 1 let let VERB ejpam-2219 28 2 g g PRON ejpam-2219 28 3 be be AUX ejpam-2219 28 4 a a DET ejpam-2219 28 5 lie lie NOUN ejpam-2219 28 6 group group NOUN ejpam-2219 28 7 ( ( PUNCT ejpam-2219 28 8 referred refer VERB ejpam-2219 28 9 to to ADP ejpam-2219 28 10 as as ADP ejpam-2219 28 11 the the DET ejpam-2219 28 12 gauge gauge NOUN ejpam-2219 28 13 group group NOUN ejpam-2219 28 14 ) ) PUNCT ejpam-2219 28 15 with with ADP ejpam-2219 28 16 lie lie NOUN ejpam-2219 28 17 algebra algebra NOUN ejpam-2219 28 18 ( ( PUNCT ejpam-2219 28 19 lg lg NOUN ejpam-2219 28 20 ) ) PUNCT ejpam-2219 28 21 and and CCONJ ejpam-2219 28 22 let let VERB ejpam-2219 28 23 { { PUNCT ejpam-2219 28 24 xµ}µ=1,2,3,4be xµ}µ=1,2,3,4be PROPN ejpam-2219 28 25 coordinates coordinate VERB ejpam-2219 28 26 on on ADP ejpam-2219 28 27 a a DET ejpam-2219 28 28 fourdimensional fourdimensional ADJ ejpam-2219 28 29 manifold manifold NOUN ejpam-2219 28 30 m m VERB ejpam-2219 28 31 which which PRON ejpam-2219 28 32 can can AUX ejpam-2219 28 33 be be AUX ejpam-2219 28 34 r4 r4 ADJ ejpam-2219 28 35 , , PUNCT ejpam-2219 28 36 r1,3 r1,3 NOUN ejpam-2219 28 37 or or CCONJ ejpam-2219 28 38 r2,2 r2,2 PROPN ejpam-2219 28 39 . . PUNCT ejpam-2219 29 1 given give VERB ejpam-2219 29 2 the the DET ejpam-2219 29 3 gauge gauge ADJ ejpam-2219 29 4 potential potential NOUN ejpam-2219 29 5 aµ(x aµ(x PUNCT ejpam-2219 29 6 ) ) PUNCT ejpam-2219 29 7 ∈ ∈ PROPN ejpam-2219 29 8 lg lg NOUN ejpam-2219 29 9 , , PUNCT ejpam-2219 29 10 we we PRON ejpam-2219 29 11 introduce introduce VERB ejpam-2219 29 12 the the DET ejpam-2219 29 13 covariant covariant ADJ ejpam-2219 29 14 derivatives derivative NOUN ejpam-2219 29 15 dµ dµ ADJ ejpam-2219 29 16 = = PUNCT ejpam-2219 29 17 ∂µ ∂µ PROPN ejpam-2219 29 18 −aµ −aµ PROPN ejpam-2219 29 19 ( ( PUNCT ejpam-2219 29 20 1 1 NUM ejpam-2219 29 21 ) ) PUNCT ejpam-2219 29 22 and and CCONJ ejpam-2219 29 23 their their PRON ejpam-2219 29 24 commutators commutator NOUN ejpam-2219 29 25 fµν fµν VERB ejpam-2219 29 26 = = SYM ejpam-2219 29 27 −[dµ −[dµ NOUN ejpam-2219 29 28 , , PUNCT ejpam-2219 29 29 dν dν VERB ejpam-2219 29 30 ] ] PUNCT ejpam-2219 29 31 = = PUNCT ejpam-2219 29 32 ∂µaν ∂µaν NUM ejpam-2219 29 33 − − PROPN ejpam-2219 29 34 ∂νaµ ∂νaµ PUNCT ejpam-2219 29 35 − − PROPN ejpam-2219 30 1 [ [ X ejpam-2219 30 2 aµ aµ PROPN ejpam-2219 30 3 , , PUNCT ejpam-2219 30 4 aν aν NOUN ejpam-2219 30 5 ] ] X ejpam-2219 30 6 , , PUNCT ejpam-2219 30 7 ( ( PUNCT ejpam-2219 30 8 2 2 X ejpam-2219 30 9 ) ) PUNCT ejpam-2219 30 10 where where SCONJ ejpam-2219 30 11 fµν fµν PRON ejpam-2219 30 12 are be AUX ejpam-2219 30 13 the the DET ejpam-2219 30 14 gauge gauge ADJ ejpam-2219 30 15 field field NOUN ejpam-2219 30 16 strengths strength NOUN ejpam-2219 30 17 . . PUNCT ejpam-2219 31 1 the the DET ejpam-2219 31 2 yangmills yangmills PROPN ejpam-2219 31 3 equations equation NOUN ejpam-2219 31 4 are be AUX ejpam-2219 31 5 a a DET ejpam-2219 31 6 set set NOUN ejpam-2219 31 7 of of ADP ejpam-2219 31 8 coupled couple VERB ejpam-2219 31 9 , , PUNCT ejpam-2219 31 10 second second ADJ ejpam-2219 31 11 - - PUNCT ejpam-2219 31 12 order order NOUN ejpam-2219 31 13 nlpdes nlpde NOUN ejpam-2219 31 14 in in ADP ejpam-2219 31 15 four four NUM ejpam-2219 31 16 dimensions dimension NOUN ejpam-2219 31 17 for for ADP ejpam-2219 31 18 the the DET ejpam-2219 31 19 lg lg NOUN ejpam-2219 31 20 - - PUNCT ejpam-2219 31 21 valued value VERB ejpam-2219 31 22 gauge gauge NOUN ejpam-2219 31 23 potential potential ADJ ejpam-2219 31 24 functionsaµ functionsaµ NOUN ejpam-2219 31 25 ’s ’s PART ejpam-2219 31 26 , , PUNCT ejpam-2219 31 27 and and CCONJ ejpam-2219 31 28 are be AUX ejpam-2219 31 29 extremely extremely ADV ejpam-2219 31 30 difficult difficult ADJ ejpam-2219 31 31 to to PART ejpam-2219 31 32 solve solve VERB ejpam-2219 31 33 in in ADP ejpam-2219 31 34 general general ADJ ejpam-2219 31 35 . . PUNCT ejpam-2219 32 1 it it PRON ejpam-2219 32 2 is be AUX ejpam-2219 32 3 however however ADV ejpam-2219 32 4 possible possible ADJ ejpam-2219 32 5 to to PART ejpam-2219 32 6 obtain obtain VERB ejpam-2219 32 7 a a DET ejpam-2219 32 8 special special ADJ ejpam-2219 32 9 class class NOUN ejpam-2219 32 10 of of ADP ejpam-2219 32 11 first first ADJ ejpam-2219 32 12 - - PUNCT ejpam-2219 32 13 order order NOUN ejpam-2219 32 14 reductions reduction NOUN ejpam-2219 32 15 of of ADP ejpam-2219 32 16 the the DET ejpam-2219 32 17 full full ADJ ejpam-2219 32 18 yang yang PROPN ejpam-2219 32 19 - - PUNCT ejpam-2219 32 20 mills mill NOUN ejpam-2219 32 21 equations equation NOUN ejpam-2219 32 22 by by ADP ejpam-2219 32 23 noting note VERB ejpam-2219 32 24 that that SCONJ ejpam-2219 32 25 any any DET ejpam-2219 32 26 fµν fµν NOUN ejpam-2219 32 27 that that PRON ejpam-2219 32 28 satisfies satisfy VERB ejpam-2219 32 29 λfµν λfµν ADV ejpam-2219 32 30 = = SYM ejpam-2219 32 31 ∗fµν ∗fµν PROPN ejpam-2219 32 32 , , PUNCT ejpam-2219 32 33 λ λ X ejpam-2219 32 34 = = PRON ejpam-2219 32 35 { { PUNCT ejpam-2219 32 36 ±1 ±1 VERB ejpam-2219 32 37 on on ADP ejpam-2219 32 38 r4 r4 PROPN ejpam-2219 32 39 , , PUNCT ejpam-2219 32 40 r2,2 r2,2 PROPN ejpam-2219 32 41 , , PUNCT ejpam-2219 32 42 ±i ±i PROPN ejpam-2219 32 43 on on ADP ejpam-2219 32 44 r3,1 r3,1 PROPN ejpam-2219 32 45 . . PUNCT ejpam-2219 33 1 ( ( PUNCT ejpam-2219 33 2 3 3 X ejpam-2219 33 3 ) ) PUNCT ejpam-2219 33 4 a.r a.r PROPN ejpam-2219 33 5 . . PROPN ejpam-2219 33 6 shehata shehata PROPN ejpam-2219 33 7 , , PUNCT ejpam-2219 33 8 j.f.alzaidy j.f.alzaidy ADJ ejpam-2219 33 9 / / SYM ejpam-2219 33 10 eur eur PROPN ejpam-2219 33 11 . . PUNCT ejpam-2219 34 1 j. j. PROPN ejpam-2219 34 2 pure pure PROPN ejpam-2219 34 3 appl appl PROPN ejpam-2219 34 4 . . PROPN ejpam-2219 34 5 math math PROPN ejpam-2219 34 6 , , PUNCT ejpam-2219 34 7 10 10 NUM ejpam-2219 34 8 ( ( PUNCT ejpam-2219 34 9 3 3 NUM ejpam-2219 34 10 ) ) PUNCT ejpam-2219 34 11 ( ( PUNCT ejpam-2219 34 12 2017 2017 NUM ejpam-2219 34 13 ) ) PUNCT ejpam-2219 34 14 , , PUNCT ejpam-2219 34 15 563 563 NUM ejpam-2219 34 16 - - SYM ejpam-2219 34 17 573 573 NUM ejpam-2219 34 18 565 565 NUM ejpam-2219 34 19 all all DET ejpam-2219 34 20 real real ADJ ejpam-2219 34 21 solutions solution NOUN ejpam-2219 34 22 of of ADP ejpam-2219 34 23 the the DET ejpam-2219 34 24 equations equation NOUN ejpam-2219 34 25 ∗fµν ∗fµν PRON ejpam-2219 34 26 = = SYM ejpam-2219 34 27 ±ifµν ±ifµν PROPN ejpam-2219 34 28 are be AUX ejpam-2219 34 29 trivial trivial ADJ ejpam-2219 34 30 . . PUNCT ejpam-2219 35 1 on on ADP ejpam-2219 35 2 r4 r4 NOUN ejpam-2219 35 3 and and CCONJ ejpam-2219 35 4 r2,2 r2,2 PROPN ejpam-2219 35 5 , , PUNCT ejpam-2219 35 6 the the DET ejpam-2219 35 7 equations equation NOUN ejpam-2219 35 8 ∗fµν ∗fµν PUNCT ejpam-2219 35 9 = = PUNCT ejpam-2219 35 10 ( ( PUNCT ejpam-2219 35 11 −)fµν −)fµν PROPN ejpam-2219 35 12 are be AUX ejpam-2219 35 13 called call VERB ejpam-2219 35 14 the the DET ejpam-2219 35 15 ( ( PUNCT ejpam-2219 35 16 anti anti ADJ ejpam-2219 35 17 ) ) PUNCT ejpam-2219 35 18 sdym sdym ADJ ejpam-2219 35 19 equations equation NOUN ejpam-2219 35 20 . . PUNCT ejpam-2219 36 1 now now ADV ejpam-2219 36 2 consider consider VERB ejpam-2219 36 3 four four NUM ejpam-2219 36 4 complex complex ADJ ejpam-2219 36 5 variables variable NOUN ejpam-2219 36 6 y y PROPN ejpam-2219 36 7 , , PUNCT ejpam-2219 36 8 ȳ ȳ PROPN ejpam-2219 36 9 , , PUNCT ejpam-2219 36 10 z z NOUN ejpam-2219 36 11 and and CCONJ ejpam-2219 36 12 z̄ z̄ PROPN ejpam-2219 36 13 defined define VERB ejpam-2219 36 14 in in ADP ejpam-2219 36 15 [ [ X ejpam-2219 36 16 27 27 NUM ejpam-2219 36 17 ] ] SYM ejpam-2219 36 18 √ √ PROPN ejpam-2219 36 19 2y 2y PROPN ejpam-2219 37 1 = = SYM ejpam-2219 37 2 x1 x1 PROPN ejpam-2219 37 3 + + PROPN ejpam-2219 37 4 ix2 ix2 PROPN ejpam-2219 37 5 , , PUNCT ejpam-2219 37 6 √ √ PROPN ejpam-2219 37 7 2ȳ 2ȳ NUM ejpam-2219 38 1 = = SYM ejpam-2219 38 2 x1 x1 PROPN ejpam-2219 38 3 − − PROPN ejpam-2219 38 4 ix2 ix2 PROPN ejpam-2219 38 5 , , PUNCT ejpam-2219 38 6 √ √ ADV ejpam-2219 38 7 2z 2z NUM ejpam-2219 38 8 = = SYM ejpam-2219 38 9 x3 x3 ADJ ejpam-2219 38 10 − − NOUN ejpam-2219 38 11 ix4 ix4 VERB ejpam-2219 38 12 , , PUNCT ejpam-2219 38 13 √ √ PROPN ejpam-2219 38 14 2z̄ 2z̄ NUM ejpam-2219 38 15 = = PUNCT ejpam-2219 39 1 x3 x3 VERB ejpam-2219 39 2 + + CCONJ ejpam-2219 39 3 ix4 ix4 VERB ejpam-2219 39 4 , , PUNCT ejpam-2219 39 5 ( ( PUNCT ejpam-2219 39 6 4 4 X ejpam-2219 39 7 ) ) PUNCT ejpam-2219 39 8 it it PRON ejpam-2219 39 9 is be AUX ejpam-2219 39 10 simple simple ADJ ejpam-2219 39 11 to to PART ejpam-2219 39 12 check check VERB ejpam-2219 39 13 that that SCONJ ejpam-2219 39 14 the the DET ejpam-2219 39 15 self self NOUN ejpam-2219 39 16 - - PUNCT ejpam-2219 39 17 duality duality NOUN ejpam-2219 39 18 equations equation NOUN ejpam-2219 39 19 fµν fµν VERB ejpam-2219 39 20 = = SYM ejpam-2219 40 1 ∗fµν ∗fµν PRON ejpam-2219 40 2 reduces reduce VERB ejpam-2219 40 3 to to PART ejpam-2219 40 4 fyz fyz VERB ejpam-2219 40 5 = = PROPN ejpam-2219 40 6 0 0 NUM ejpam-2219 40 7 , , PUNCT ejpam-2219 40 8 fȳz̄ fȳz̄ NOUN ejpam-2219 40 9 = = SYM ejpam-2219 40 10 0 0 NUM ejpam-2219 40 11 , , PUNCT ejpam-2219 40 12 fyȳ fyȳ NOUN ejpam-2219 41 1 + + X ejpam-2219 41 2 fzz̄ fzz̄ X ejpam-2219 41 3 = = SYM ejpam-2219 41 4 0 0 X ejpam-2219 41 5 . . PUNCT ejpam-2219 41 6 ( ( PUNCT ejpam-2219 41 7 5 5 X ejpam-2219 41 8 ) ) PUNCT ejpam-2219 41 9 equations equation NOUN ejpam-2219 41 10 ( ( PUNCT ejpam-2219 41 11 5 5 NUM ejpam-2219 41 12 ) ) PUNCT ejpam-2219 41 13 are be AUX ejpam-2219 41 14 the the DET ejpam-2219 41 15 compatibility compatibility NOUN ejpam-2219 41 16 condition condition NOUN ejpam-2219 41 17 of of ADP ejpam-2219 41 18 the the DET ejpam-2219 41 19 linear linear ADJ ejpam-2219 41 20 problem problem NOUN ejpam-2219 41 21 [ [ X ejpam-2219 41 22 29 29 NUM ejpam-2219 41 23 ] ] PUNCT ejpam-2219 41 24 ( ( PUNCT ejpam-2219 41 25 ψy ψy PROPN ejpam-2219 41 26 + + NUM ejpam-2219 41 27 iζψz̄ iζψz̄ NOUN ejpam-2219 41 28 ) ) PUNCT ejpam-2219 41 29 = = SYM ejpam-2219 42 1 ( ( PUNCT ejpam-2219 42 2 ay ay PROPN ejpam-2219 42 3 + + PROPN ejpam-2219 42 4 iζaz̄)ψ iζaz̄)ψ PROPN ejpam-2219 42 5 , , PUNCT ejpam-2219 42 6 ( ( PUNCT ejpam-2219 42 7 6 6 NUM ejpam-2219 42 8 ) ) PUNCT ejpam-2219 42 9 ( ( PUNCT ejpam-2219 42 10 ψz ψz NOUN ejpam-2219 42 11 − − NOUN ejpam-2219 42 12 iζψȳ iζψȳ NUM ejpam-2219 42 13 ) ) PUNCT ejpam-2219 42 14 = = SYM ejpam-2219 42 15 ( ( PUNCT ejpam-2219 42 16 az az PROPN ejpam-2219 42 17 − − PROPN ejpam-2219 42 18 iζaȳ)ψ iζaȳ)ψ PROPN ejpam-2219 42 19 , , PUNCT ejpam-2219 42 20 ( ( PUNCT ejpam-2219 42 21 7 7 X ejpam-2219 42 22 ) ) PUNCT ejpam-2219 42 23 where where SCONJ ejpam-2219 42 24 ζ ζ NOUN ejpam-2219 42 25 is be AUX ejpam-2219 42 26 a a DET ejpam-2219 42 27 parameter parameter NOUN ejpam-2219 42 28 , , PUNCT ejpam-2219 42 29 independent independent ADJ ejpam-2219 42 30 of of ADP ejpam-2219 42 31 y y PROPN ejpam-2219 42 32 , , PUNCT ejpam-2219 42 33 ȳ ȳ PROPN ejpam-2219 42 34 , , PUNCT ejpam-2219 42 35 z z NOUN ejpam-2219 42 36 and and CCONJ ejpam-2219 42 37 z̄. z̄. PROPN ejpam-2219 42 38 the the DET ejpam-2219 42 39 compatibility compatibility NOUN ejpam-2219 42 40 condition condition NOUN ejpam-2219 42 41 is be AUX ejpam-2219 42 42 simply simply ADV ejpam-2219 42 43 ( ( PUNCT ejpam-2219 42 44 ∂z ∂z PROPN ejpam-2219 42 45 − − PROPN ejpam-2219 42 46 iζ∂ȳ)(∂y iζ∂ȳ)(∂y VERB ejpam-2219 42 47 + + CCONJ ejpam-2219 42 48 iζ∂z̄)ψ iζ∂z̄)ψ NOUN ejpam-2219 42 49 = = SYM ejpam-2219 42 50 ( ( PUNCT ejpam-2219 42 51 ∂y ∂y X ejpam-2219 42 52 + + CCONJ ejpam-2219 42 53 iζ∂z̄)(∂z iζ∂z̄)(∂z VERB ejpam-2219 42 54 − − PROPN ejpam-2219 42 55 iζ∂ȳ)ψ iζ∂ȳ)ψ NOUN ejpam-2219 42 56 . . PUNCT ejpam-2219 43 1 ( ( PUNCT ejpam-2219 43 2 8) 8) NUM ejpam-2219 43 3 on on ADP ejpam-2219 43 4 using use VERB ejpam-2219 43 5 equations equation NOUN ejpam-2219 43 6 ( ( PUNCT ejpam-2219 43 7 6 6 NUM ejpam-2219 43 8 ) ) PUNCT ejpam-2219 43 9 and and CCONJ ejpam-2219 43 10 ( ( PUNCT ejpam-2219 43 11 7 7 NUM ejpam-2219 43 12 ) ) PUNCT ejpam-2219 43 13 , , PUNCT ejpam-2219 43 14 this this PRON ejpam-2219 43 15 gives give VERB ejpam-2219 43 16 [ [ PUNCT ejpam-2219 43 17 fyz fyz NOUN ejpam-2219 43 18 − − PROPN ejpam-2219 43 19 iζ(fyȳ iζ(fyȳ NOUN ejpam-2219 44 1 + + NUM ejpam-2219 44 2 fzz̄)− fzz̄)− NOUN ejpam-2219 44 3 ζ2fȳz̄]ψ ζ2fȳz̄]ψ PROPN ejpam-2219 44 4 = = PROPN ejpam-2219 44 5 0 0 PROPN ejpam-2219 44 6 . . NUM ejpam-2219 44 7 , , PUNCT ejpam-2219 44 8 ( ( PUNCT ejpam-2219 44 9 9 9 X ejpam-2219 44 10 ) ) PUNCT ejpam-2219 44 11 equations equation NOUN ejpam-2219 44 12 ( ( PUNCT ejpam-2219 44 13 5 5 X ejpam-2219 44 14 ) ) PUNCT ejpam-2219 44 15 can can AUX ejpam-2219 44 16 be be AUX ejpam-2219 44 17 immediately immediately ADV ejpam-2219 44 18 integrated integrate VERB ejpam-2219 44 19 , , PUNCT ejpam-2219 44 20 since since SCONJ ejpam-2219 44 21 they they PRON ejpam-2219 44 22 are be AUX ejpam-2219 44 23 pure pure ADJ ejpam-2219 44 24 gauge gauge NOUN ejpam-2219 44 25 , , PUNCT ejpam-2219 44 26 to to PART ejpam-2219 44 27 give give VERB ejpam-2219 44 28 ay ay NOUN ejpam-2219 44 29 = = SYM ejpam-2219 44 30 d−1dy d−1dy PROPN ejpam-2219 44 31 , , PUNCT ejpam-2219 44 32 az az PROPN ejpam-2219 44 33 = = PUNCT ejpam-2219 44 34 d−1dz d−1dz PROPN ejpam-2219 44 35 , , PUNCT ejpam-2219 44 36 aȳ aȳ VERB ejpam-2219 45 1 = = PUNCT ejpam-2219 45 2 d̄−1d̄ȳ d̄−1d̄ȳ PROPN ejpam-2219 45 3 , , PUNCT ejpam-2219 45 4 az̄ az̄ ADV ejpam-2219 45 5 = = SYM ejpam-2219 45 6 d̄−1d̄z̄ d̄−1d̄z̄ PROPN ejpam-2219 45 7 , , PUNCT ejpam-2219 45 8 ( ( PUNCT ejpam-2219 45 9 10 10 NUM ejpam-2219 45 10 ) ) PUNCT ejpam-2219 45 11 where where SCONJ ejpam-2219 45 12 d d NOUN ejpam-2219 45 13 and and CCONJ ejpam-2219 45 14 d̄ d̄ NOUN ejpam-2219 45 15 are be AUX ejpam-2219 45 16 arbitrary arbitrary ADJ ejpam-2219 45 17 2×2 2×2 NUM ejpam-2219 45 18 complex complex ADJ ejpam-2219 45 19 matrix matrix NOUN ejpam-2219 45 20 functions function NOUN ejpam-2219 45 21 of of ADP ejpam-2219 45 22 y y PROPN ejpam-2219 45 23 , , PUNCT ejpam-2219 45 24 ȳ ȳ PROPN ejpam-2219 45 25 , , PUNCT ejpam-2219 45 26 z z NOUN ejpam-2219 45 27 and and CCONJ ejpam-2219 45 28 z̄ z̄ PROPN ejpam-2219 45 29 with with ADP ejpam-2219 45 30 determinant determinant ADJ ejpam-2219 45 31 = = SYM ejpam-2219 45 32 1 1 NUM ejpam-2219 45 33 ( ( PUNCT ejpam-2219 45 34 for for ADP ejpam-2219 45 35 su(2 su(2 NOUN ejpam-2219 45 36 ) ) PUNCT ejpam-2219 45 37 gauge gauge NOUN ejpam-2219 45 38 group group NOUN ejpam-2219 45 39 ) ) PUNCT ejpam-2219 45 40 and and CCONJ ejpam-2219 45 41 dy dy NOUN ejpam-2219 45 42 = = PROPN ejpam-2219 45 43 ∂yd ∂yd PROPN ejpam-2219 45 44 , , PUNCT ejpam-2219 45 45 etc etc X ejpam-2219 45 46 . . X ejpam-2219 45 47 for for ADP ejpam-2219 45 48 real real ADJ ejpam-2219 45 49 gauge gauge NOUN ejpam-2219 45 50 fields field NOUN ejpam-2219 45 51 aµ=̇−a+ aµ=̇−a+ X ejpam-2219 45 52 m m VERB ejpam-2219 45 53 ( ( PUNCT ejpam-2219 45 54 the the DET ejpam-2219 45 55 symbol symbol NOUN ejpam-2219 45 56 = = SYM ejpam-2219 45 57 ̇ ̇ NOUN ejpam-2219 45 58 is be AUX ejpam-2219 45 59 used use VERB ejpam-2219 45 60 for for ADP ejpam-2219 45 61 equations equation NOUN ejpam-2219 45 62 valid valid ADJ ejpam-2219 45 63 only only ADV ejpam-2219 45 64 for for ADP ejpam-2219 45 65 real real ADJ ejpam-2219 45 66 values value NOUN ejpam-2219 45 67 of of ADP ejpam-2219 45 68 x1 x1 PROPN ejpam-2219 45 69 , , PUNCT ejpam-2219 45 70 x2 x2 PROPN ejpam-2219 45 71 , , PUNCT ejpam-2219 45 72 x3and x3and PROPN ejpam-2219 45 73 x4 x4 PROPN ejpam-2219 45 74 ) ) PUNCT ejpam-2219 45 75 , , PUNCT ejpam-2219 45 76 we we PRON ejpam-2219 45 77 require require VERB ejpam-2219 45 78 d̄=̇(d+)−1 d̄=̇(d+)−1 NOUN ejpam-2219 45 79 . . PUNCT ejpam-2219 46 1 ( ( PUNCT ejpam-2219 46 2 11 11 NUM ejpam-2219 46 3 ) ) PUNCT ejpam-2219 46 4 gauge gauge NOUN ejpam-2219 46 5 transformations transformation NOUN ejpam-2219 46 6 are be AUX ejpam-2219 46 7 the the DET ejpam-2219 46 8 transformations transformation NOUN ejpam-2219 46 9 d d X ejpam-2219 46 10 → → SYM ejpam-2219 46 11 du du PROPN ejpam-2219 46 12 , , PUNCT ejpam-2219 46 13 d̄ d̄ PROPN ejpam-2219 46 14 → → SYM ejpam-2219 46 15 d̄u d̄u PROPN ejpam-2219 46 16 , , PUNCT ejpam-2219 46 17 u+u=̇i u+u=̇i X ejpam-2219 46 18 , , PUNCT ejpam-2219 46 19 ( ( PUNCT ejpam-2219 46 20 12 12 NUM ejpam-2219 46 21 ) ) PUNCT ejpam-2219 46 22 where where SCONJ ejpam-2219 46 23 u u NOUN ejpam-2219 46 24 is be AUX ejpam-2219 46 25 a a DET ejpam-2219 46 26 2×2 2×2 NUM ejpam-2219 46 27 matrix matrix NOUN ejpam-2219 46 28 function function NOUN ejpam-2219 46 29 of of ADP ejpam-2219 46 30 y y PROPN ejpam-2219 46 31 , , PUNCT ejpam-2219 46 32 ȳ ȳ PROPN ejpam-2219 46 33 , , PUNCT ejpam-2219 46 34 z z PROPN ejpam-2219 46 35 , , PUNCT ejpam-2219 46 36 z̄ z̄ PROPN ejpam-2219 46 37 with with ADP ejpam-2219 46 38 determined determined ADJ ejpam-2219 46 39 = = SYM ejpam-2219 46 40 1 1 X ejpam-2219 46 41 . . PUNCT ejpam-2219 47 1 under under ADP ejpam-2219 47 2 transformation transformation NOUN ejpam-2219 47 3 ( ( PUNCT ejpam-2219 47 4 12 12 NUM ejpam-2219 47 5 ) ) PUNCT ejpam-2219 47 6 , , PUNCT ejpam-2219 47 7 equation equation NOUN ejpam-2219 47 8 ( ( PUNCT ejpam-2219 47 9 11 11 NUM ejpam-2219 47 10 ) ) PUNCT ejpam-2219 47 11 remains remain VERB ejpam-2219 47 12 unchanged unchanged ADJ ejpam-2219 47 13 . . PUNCT ejpam-2219 48 1 we we PRON ejpam-2219 48 2 now now ADV ejpam-2219 48 3 define define VERB ejpam-2219 48 4 the the DET ejpam-2219 48 5 hermitian hermitian ADJ ejpam-2219 48 6 matrix matrix NOUN ejpam-2219 48 7 j j PROPN ejpam-2219 48 8 as as ADP ejpam-2219 48 9 j j PROPN ejpam-2219 48 10 = = SYM ejpam-2219 48 11 dd̄−1=̇dd+ dd̄−1=̇dd+ PROPN ejpam-2219 48 12 . . PUNCT ejpam-2219 49 1 ( ( PUNCT ejpam-2219 49 2 13 13 NUM ejpam-2219 49 3 ) ) PUNCT ejpam-2219 49 4 j j PROPN ejpam-2219 49 5 has have VERB ejpam-2219 49 6 the the DET ejpam-2219 49 7 very very ADV ejpam-2219 49 8 important important ADJ ejpam-2219 49 9 property property NOUN ejpam-2219 49 10 of of ADP ejpam-2219 49 11 being be AUX ejpam-2219 49 12 invariant invariant ADJ ejpam-2219 49 13 under under ADP ejpam-2219 49 14 the the DET ejpam-2219 49 15 gauge gauge ADJ ejpam-2219 49 16 transformation transformation NOUN ejpam-2219 49 17 ( ( PUNCT ejpam-2219 49 18 12 12 NUM ejpam-2219 49 19 ) ) PUNCT ejpam-2219 49 20 . . PUNCT ejpam-2219 50 1 the the DET ejpam-2219 50 2 only only ADJ ejpam-2219 50 3 non non ADJ ejpam-2219 50 4 vanishing vanish VERB ejpam-2219 50 5 field field NOUN ejpam-2219 50 6 strengths strength NOUN ejpam-2219 50 7 in in ADP ejpam-2219 50 8 terms term NOUN ejpam-2219 50 9 of of ADP ejpam-2219 50 10 j j PROPN ejpam-2219 50 11 becomes become VERB ejpam-2219 50 12 fuv̄ fuv̄ PUNCT ejpam-2219 51 1 = = PUNCT ejpam-2219 51 2 −d̄−1(j −d̄−1(j ADJ ejpam-2219 51 3 −1ju)v̄d̄. −1ju)v̄d̄. NOUN ejpam-2219 51 4 ( ( PUNCT ejpam-2219 51 5 14 14 NUM ejpam-2219 51 6 ) ) PUNCT ejpam-2219 51 7 a.r a.r PROPN ejpam-2219 51 8 . . PROPN ejpam-2219 51 9 shehata shehata PROPN ejpam-2219 51 10 , , PUNCT ejpam-2219 51 11 j.f.alzaidy j.f.alzaidy ADJ ejpam-2219 51 12 / / SYM ejpam-2219 51 13 eur eur PROPN ejpam-2219 51 14 . . PUNCT ejpam-2219 52 1 j. j. PROPN ejpam-2219 52 2 pure pure PROPN ejpam-2219 52 3 appl appl PROPN ejpam-2219 52 4 . . PROPN ejpam-2219 52 5 math math PROPN ejpam-2219 52 6 , , PUNCT ejpam-2219 52 7 10 10 NUM ejpam-2219 52 8 ( ( PUNCT ejpam-2219 52 9 3 3 NUM ejpam-2219 52 10 ) ) PUNCT ejpam-2219 52 11 ( ( PUNCT ejpam-2219 52 12 2017 2017 NUM ejpam-2219 52 13 ) ) PUNCT ejpam-2219 52 14 , , PUNCT ejpam-2219 52 15 563 563 NUM ejpam-2219 52 16 - - SYM ejpam-2219 52 17 573 573 NUM ejpam-2219 52 18 566 566 NUM ejpam-2219 52 19 ( ( PUNCT ejpam-2219 52 20 u u NOUN ejpam-2219 52 21 , , PUNCT ejpam-2219 52 22 v v NOUN ejpam-2219 52 23 = = SYM ejpam-2219 52 24 y y PROPN ejpam-2219 52 25 , , PUNCT ejpam-2219 52 26 z z NOUN ejpam-2219 52 27 ) ) PUNCT ejpam-2219 52 28 and and CCONJ ejpam-2219 52 29 the the DET ejpam-2219 52 30 remaining remain VERB ejpam-2219 52 31 self self NOUN ejpam-2219 52 32 - - PUNCT ejpam-2219 52 33 duality duality NOUN ejpam-2219 52 34 equation equation NOUN ejpam-2219 52 35 ( ( PUNCT ejpam-2219 52 36 5 5 X ejpam-2219 52 37 ) ) PUNCT ejpam-2219 52 38 takes take VERB ejpam-2219 52 39 the the DET ejpam-2219 52 40 form form NOUN ejpam-2219 52 41 ( ( PUNCT ejpam-2219 52 42 j j PROPN ejpam-2219 52 43 −1jy)ȳ −1jy)ȳ PROPN ejpam-2219 52 44 + + CCONJ ejpam-2219 52 45 ( ( PUNCT ejpam-2219 52 46 j j PROPN ejpam-2219 52 47 −1jz)z̄ −1jz)z̄ PROPN ejpam-2219 52 48 = = NOUN ejpam-2219 52 49 0 0 PROPN ejpam-2219 52 50 . . PUNCT ejpam-2219 53 1 ( ( PUNCT ejpam-2219 53 2 15 15 NUM ejpam-2219 53 3 ) ) PUNCT ejpam-2219 53 4 the the DET ejpam-2219 53 5 action action NOUN ejpam-2219 53 6 density density NOUN ejpam-2219 53 7 in in ADP ejpam-2219 53 8 terms term NOUN ejpam-2219 53 9 of of ADP ejpam-2219 53 10 j j PROPN ejpam-2219 53 11 is be AUX ejpam-2219 53 12 φ(j φ(j PROPN ejpam-2219 53 13 ) ) PUNCT ejpam-2219 53 14 = = SYM ejpam-2219 54 1 −1 −1 NOUN ejpam-2219 54 2 2 2 NUM ejpam-2219 54 3 trfµνfµν trfµνfµν NOUN ejpam-2219 54 4 = = SYM ejpam-2219 54 5 −2tr(fyȳfzz̄ −2tr(fyȳfzz̄ NOUN ejpam-2219 54 6 + + CCONJ ejpam-2219 54 7 fyz̄fȳz fyz̄fȳz PROPN ejpam-2219 54 8 ) ) PUNCT ejpam-2219 54 9 = = PUNCT ejpam-2219 55 1 −2tr{(j −2tr{(j X ejpam-2219 55 2 −1jy)ȳ(j −1jy)ȳ(j X ejpam-2219 55 3 −1jz)z̄ −1jz)z̄ PROPN ejpam-2219 55 4 − − PROPN ejpam-2219 55 5 ( ( PUNCT ejpam-2219 55 6 j j PROPN ejpam-2219 55 7 −1jy)z̄(j −1jy)z̄(j X ejpam-2219 55 8 −1jz)ȳ −1jz)ȳ PROPN ejpam-2219 55 9 } } PUNCT ejpam-2219 55 10 . . PUNCT ejpam-2219 56 1 ( ( PUNCT ejpam-2219 56 2 16 16 NUM ejpam-2219 56 3 ) ) PUNCT ejpam-2219 56 4 in in ADP ejpam-2219 56 5 this this DET ejpam-2219 56 6 paper paper NOUN ejpam-2219 56 7 , , PUNCT ejpam-2219 56 8 the the DET ejpam-2219 56 9 canonical canonical ADJ ejpam-2219 56 10 reduction reduction NOUN ejpam-2219 56 11 of of ADP ejpam-2219 56 12 four four NUM ejpam-2219 56 13 dimensional dimensional ADJ ejpam-2219 56 14 self self NOUN ejpam-2219 56 15 - - PUNCT ejpam-2219 56 16 dual dual ADJ ejpam-2219 56 17 yang yang PROPN ejpam-2219 56 18 - - PUNCT ejpam-2219 56 19 mills mill NOUN ejpam-2219 56 20 theory theory NOUN ejpam-2219 56 21 to to ADP ejpam-2219 56 22 two two NUM ejpam-2219 56 23 dimensional dimensional ADJ ejpam-2219 56 24 complex complex ADJ ejpam-2219 56 25 ginzburg ginzburg NOUN ejpam-2219 56 26 - - PUNCT ejpam-2219 56 27 landau landau NOUN ejpam-2219 56 28 ( ( PUNCT ejpam-2219 56 29 cgl cgl NOUN ejpam-2219 56 30 ) ) PUNCT ejpam-2219 56 31 equation equation NOUN ejpam-2219 56 32 are be AUX ejpam-2219 56 33 considered consider VERB ejpam-2219 56 34 . . PUNCT ejpam-2219 57 1 we we PRON ejpam-2219 57 2 give give VERB ejpam-2219 57 3 a a DET ejpam-2219 57 4 new new NOUN ejpam-2219 57 5 of of ADP ejpam-2219 57 6 exact exact ADJ ejpam-2219 57 7 solution solution NOUN ejpam-2219 57 8 for for ADP ejpam-2219 57 9 the the DET ejpam-2219 57 10 cgl cgl PROPN ejpam-2219 57 11 equation equation NOUN ejpam-2219 57 12 by by ADP ejpam-2219 57 13 applying apply VERB ejpam-2219 57 14 the the DET ejpam-2219 57 15 bts bt NOUN ejpam-2219 57 16 method method NOUN ejpam-2219 57 17 with with ADP ejpam-2219 57 18 the the DET ejpam-2219 57 19 aid aid NOUN ejpam-2219 57 20 of of ADP ejpam-2219 57 21 mathematica mathematica PROPN ejpam-2219 58 1 [ [ X ejpam-2219 58 2 28 28 NUM ejpam-2219 58 3 , , PUNCT ejpam-2219 58 4 11 11 NUM ejpam-2219 58 5 , , PUNCT ejpam-2219 58 6 7 7 NUM ejpam-2219 58 7 , , PUNCT ejpam-2219 58 8 8 8 NUM ejpam-2219 58 9 , , PUNCT ejpam-2219 58 10 20 20 NUM ejpam-2219 58 11 , , PUNCT ejpam-2219 58 12 1 1 NUM ejpam-2219 58 13 , , PUNCT ejpam-2219 58 14 3 3 NUM ejpam-2219 58 15 , , PUNCT ejpam-2219 58 16 2 2 NUM ejpam-2219 58 17 , , PUNCT ejpam-2219 58 18 4 4 NUM ejpam-2219 58 19 , , PUNCT ejpam-2219 58 20 5 5 NUM ejpam-2219 58 21 , , PUNCT ejpam-2219 58 22 27 27 NUM ejpam-2219 58 23 , , PUNCT ejpam-2219 58 24 29 29 NUM ejpam-2219 58 25 ] ] PUNCT ejpam-2219 58 26 . . PUNCT ejpam-2219 59 1 consequently consequently ADV ejpam-2219 59 2 we we PRON ejpam-2219 59 3 find find VERB ejpam-2219 59 4 exact exact ADJ ejpam-2219 59 5 solutions solution NOUN ejpam-2219 59 6 for for ADP ejpam-2219 59 7 self self NOUN ejpam-2219 59 8 - - PUNCT ejpam-2219 59 9 dual dual ADJ ejpam-2219 59 10 yang yang PROPN ejpam-2219 59 11 mills mills PROPN ejpam-2219 59 12 equations equation NOUN ejpam-2219 59 13 . . PUNCT ejpam-2219 60 1 in in ADP ejpam-2219 60 2 addition addition NOUN ejpam-2219 60 3 the the DET ejpam-2219 60 4 corresponding corresponding ADJ ejpam-2219 60 5 gauge gauge NOUN ejpam-2219 60 6 potential potential NOUN ejpam-2219 60 7 aµ aµ PROPN ejpam-2219 60 8 and and CCONJ ejpam-2219 60 9 the the DET ejpam-2219 60 10 gauge gauge ADJ ejpam-2219 60 11 field field NOUN ejpam-2219 60 12 strengths strength NOUN ejpam-2219 60 13 fµν fµν PRON ejpam-2219 60 14 are be AUX ejpam-2219 60 15 also also ADV ejpam-2219 60 16 obtained obtain VERB ejpam-2219 60 17 . . PUNCT ejpam-2219 61 1 the the DET ejpam-2219 61 2 paper paper NOUN ejpam-2219 61 3 is be AUX ejpam-2219 61 4 organized organize VERB ejpam-2219 61 5 as as SCONJ ejpam-2219 61 6 follows follow VERB ejpam-2219 61 7 : : PUNCT ejpam-2219 61 8 on on ADP ejpam-2219 61 9 one one NUM ejpam-2219 61 10 hand hand NOUN ejpam-2219 61 11 the the DET ejpam-2219 61 12 reduction reduction NOUN ejpam-2219 61 13 of of ADP ejpam-2219 61 14 yang yang PROPN ejpam-2219 61 15 - - PUNCT ejpam-2219 61 16 mills mill NOUN ejpam-2219 61 17 theory theory NOUN ejpam-2219 61 18 to to ADP ejpam-2219 61 19 cgl cgl NOUN ejpam-2219 61 20 equation equation NOUN ejpam-2219 61 21 , , PUNCT ejpam-2219 61 22 and and CCONJ ejpam-2219 61 23 exact exact ADJ ejpam-2219 61 24 solutions solution NOUN ejpam-2219 61 25 are be AUX ejpam-2219 61 26 presented present VERB ejpam-2219 61 27 in in ADP ejpam-2219 61 28 sections section NOUN ejpam-2219 61 29 2 2 NUM ejpam-2219 61 30 and and CCONJ ejpam-2219 61 31 3 3 NUM ejpam-2219 61 32 respectively respectively ADV ejpam-2219 61 33 . . PUNCT ejpam-2219 62 1 moreover moreover ADV ejpam-2219 62 2 the the DET ejpam-2219 62 3 gauge gauge ADJ ejpam-2219 62 4 potential potential NOUN ejpam-2219 62 5 aµ aµ PROPN ejpam-2219 62 6 and and CCONJ ejpam-2219 62 7 the the DET ejpam-2219 62 8 gauge gauge ADJ ejpam-2219 62 9 field field NOUN ejpam-2219 62 10 strengths strength NOUN ejpam-2219 62 11 fµν fµν PRON ejpam-2219 62 12 are be AUX ejpam-2219 62 13 also also ADV ejpam-2219 62 14 obtained obtain VERB ejpam-2219 62 15 . . PUNCT ejpam-2219 63 1 section section NOUN ejpam-2219 63 2 4 4 NUM ejpam-2219 63 3 contains contain VERB ejpam-2219 63 4 the the DET ejpam-2219 63 5 conclusion conclusion NOUN ejpam-2219 63 6 . . PUNCT ejpam-2219 64 1 2 2 X ejpam-2219 64 2 . . X ejpam-2219 64 3 the the DET ejpam-2219 64 4 canonical canonical ADJ ejpam-2219 64 5 reduction reduction NOUN ejpam-2219 64 6 of of ADP ejpam-2219 64 7 four four NUM ejpam-2219 64 8 - - PUNCT ejpam-2219 64 9 dimensional dimensional ADJ ejpam-2219 64 10 sdym sdym ADJ ejpam-2219 64 11 theory theory NOUN ejpam-2219 64 12 to to ADP ejpam-2219 64 13 two two NUM ejpam-2219 64 14 dimensional dimensional ADJ ejpam-2219 64 15 cgl cgl NOUN ejpam-2219 64 16 equation equation NOUN ejpam-2219 64 17 suppose suppose VERB ejpam-2219 64 18 that that SCONJ ejpam-2219 64 19 aµ aµ PROPN ejpam-2219 64 20 ’s ’s AUX ejpam-2219 64 21 depend depend VERB ejpam-2219 64 22 on on ADP ejpam-2219 64 23 x x X ejpam-2219 64 24 = = PUNCT ejpam-2219 64 25 y y PROPN ejpam-2219 64 26 + + CCONJ ejpam-2219 64 27 ȳ ȳ PROPN ejpam-2219 64 28 and and CCONJ ejpam-2219 64 29 t t NOUN ejpam-2219 64 30 = = PUNCT ejpam-2219 64 31 z z NOUN ejpam-2219 64 32 only only ADV ejpam-2219 64 33 . . PUNCT ejpam-2219 65 1 if if SCONJ ejpam-2219 65 2 we we PRON ejpam-2219 65 3 use use VERB ejpam-2219 65 4 a a DET ejpam-2219 65 5 gauge gauge NOUN ejpam-2219 65 6 in in ADP ejpam-2219 65 7 which which PRON ejpam-2219 65 8 aȳ aȳ VERB ejpam-2219 65 9 = = SYM ejpam-2219 65 10 0 0 NUM ejpam-2219 65 11 , , PUNCT ejpam-2219 65 12 in in ADP ejpam-2219 65 13 terms term NOUN ejpam-2219 65 14 of of ADP ejpam-2219 65 15 the the DET ejpam-2219 65 16 matrix matrix NOUN ejpam-2219 65 17 - - PUNCT ejpam-2219 65 18 valued value VERB ejpam-2219 65 19 functions function NOUN ejpam-2219 65 20 p p X ejpam-2219 65 21 : : PUNCT ejpam-2219 65 22 = = SYM ejpam-2219 65 23 ay ay PROPN ejpam-2219 65 24 , , PUNCT ejpam-2219 65 25 q q X ejpam-2219 65 26 : : PUNCT ejpam-2219 65 27 = = NOUN ejpam-2219 65 28 az az PROPN ejpam-2219 65 29 , , PUNCT ejpam-2219 65 30 r r NOUN ejpam-2219 65 31 : : PUNCT ejpam-2219 65 32 = = SYM ejpam-2219 65 33 az̄ az̄ PROPN ejpam-2219 65 34 , , PUNCT ejpam-2219 65 35 the the DET ejpam-2219 65 36 sdym sdym ADJ ejpam-2219 65 37 equations equation NOUN ejpam-2219 65 38 ( ( PUNCT ejpam-2219 65 39 5 5 X ejpam-2219 65 40 ) ) PUNCT ejpam-2219 65 41 are be AUX ejpam-2219 65 42 rx rx ADJ ejpam-2219 65 43 = = SYM ejpam-2219 65 44 0 0 NUM ejpam-2219 65 45 ( ( PUNCT ejpam-2219 65 46 17 17 NUM ejpam-2219 65 47 ) ) PUNCT ejpam-2219 65 48 qx qx PROPN ejpam-2219 65 49 − − PROPN ejpam-2219 65 50 pt pt NOUN ejpam-2219 65 51 − − PROPN ejpam-2219 66 1 [ [ X ejpam-2219 66 2 p p X ejpam-2219 66 3 , , PUNCT ejpam-2219 66 4 q q X ejpam-2219 66 5 ] ] X ejpam-2219 66 6 = = SYM ejpam-2219 66 7 0 0 NUM ejpam-2219 66 8 , , PUNCT ejpam-2219 66 9 ( ( PUNCT ejpam-2219 66 10 18 18 NUM ejpam-2219 66 11 ) ) PUNCT ejpam-2219 66 12 rt rt NOUN ejpam-2219 66 13 − − PROPN ejpam-2219 66 14 px px INTJ ejpam-2219 67 1 − − PROPN ejpam-2219 68 1 [ [ X ejpam-2219 68 2 q q X ejpam-2219 68 3 , , PUNCT ejpam-2219 68 4 p p X ejpam-2219 68 5 ] ] X ejpam-2219 68 6 = = SYM ejpam-2219 68 7 0 0 X ejpam-2219 68 8 . . PUNCT ejpam-2219 69 1 ( ( PUNCT ejpam-2219 69 2 19 19 NUM ejpam-2219 69 3 ) ) PUNCT ejpam-2219 69 4 let let VERB ejpam-2219 69 5 r r NOUN ejpam-2219 69 6 take take VERB ejpam-2219 69 7 the the DET ejpam-2219 69 8 canonical canonical ADJ ejpam-2219 69 9 form form NOUN ejpam-2219 69 10 r r NOUN ejpam-2219 69 11 = = PUNCT ejpam-2219 69 12 ( ( PUNCT ejpam-2219 69 13 −i −i PROPN ejpam-2219 69 14 2a 2a NUM ejpam-2219 69 15 0 0 NUM ejpam-2219 69 16 0 0 PUNCT ejpam-2219 70 1 i i PRON ejpam-2219 70 2 2a 2a NUM ejpam-2219 70 3 ) ) PUNCT ejpam-2219 70 4 . . PUNCT ejpam-2219 71 1 ( ( PUNCT ejpam-2219 71 2 20 20 X ejpam-2219 71 3 ) ) PUNCT ejpam-2219 71 4 we we PRON ejpam-2219 71 5 then then ADV ejpam-2219 71 6 find find VERB ejpam-2219 71 7 that that SCONJ ejpam-2219 71 8 p p NOUN ejpam-2219 71 9 = = X ejpam-2219 71 10 ( ( PUNCT ejpam-2219 71 11 0 0 NUM ejpam-2219 71 12 ue−iµt ue−iµt NOUN ejpam-2219 71 13 −u∗eiµt −u∗eiµt NOUN ejpam-2219 71 14 0 0 NUM ejpam-2219 71 15 ) ) PUNCT ejpam-2219 71 16 , , PUNCT ejpam-2219 71 17 ( ( PUNCT ejpam-2219 71 18 21 21 NUM ejpam-2219 71 19 ) ) PUNCT ejpam-2219 71 20 q q NOUN ejpam-2219 71 21 = = SYM ejpam-2219 71 22 ( ( PUNCT ejpam-2219 71 23 ia|u|2 ia|u|2 PROPN ejpam-2219 71 24 aiuxe aiuxe PROPN ejpam-2219 71 25 −iµt −iµt PROPN ejpam-2219 71 26 aiu∗xe aiu∗xe NOUN ejpam-2219 71 27 iµt iµt NOUN ejpam-2219 71 28 −ia|u|2 −ia|u|2 PROPN ejpam-2219 71 29 ) ) PUNCT ejpam-2219 71 30 , , PUNCT ejpam-2219 71 31 ( ( PUNCT ejpam-2219 71 32 22 22 NUM ejpam-2219 71 33 ) ) PUNCT ejpam-2219 71 34 from from ADP ejpam-2219 71 35 eq eq ADP ejpam-2219 71 36 . . PUNCT ejpam-2219 72 1 ( ( PUNCT ejpam-2219 72 2 18 18 NUM ejpam-2219 72 3 ) ) PUNCT ejpam-2219 72 4 , , PUNCT ejpam-2219 72 5 we we PRON ejpam-2219 72 6 obtain obtain VERB ejpam-2219 72 7 the the DET ejpam-2219 72 8 cgl cgl NOUN ejpam-2219 72 9 equation equation NOUN ejpam-2219 72 10 iut iut PROPN ejpam-2219 72 11 + + CCONJ ejpam-2219 72 12 auxx auxx ADJ ejpam-2219 73 1 + + CCONJ ejpam-2219 73 2 2a|u|2u+ 2a|u|2u+ NUM ejpam-2219 73 3 µu µu ADP ejpam-2219 73 4 = = NOUN ejpam-2219 73 5 0 0 PROPN ejpam-2219 73 6 , , PUNCT ejpam-2219 73 7 ( ( PUNCT ejpam-2219 73 8 23 23 NUM ejpam-2219 73 9 ) ) PUNCT ejpam-2219 73 10 where where SCONJ ejpam-2219 73 11 a a PRON ejpam-2219 73 12 is be AUX ejpam-2219 73 13 a a DET ejpam-2219 73 14 complex complex ADJ ejpam-2219 73 15 constant constant ADJ ejpam-2219 73 16 and and CCONJ ejpam-2219 73 17 µ µ NOUN ejpam-2219 73 18 is be AUX ejpam-2219 73 19 real real ADV ejpam-2219 73 20 constant constant ADJ ejpam-2219 73 21 . . PUNCT ejpam-2219 74 1 a.r a.r PROPN ejpam-2219 74 2 . . PROPN ejpam-2219 74 3 shehata shehata PROPN ejpam-2219 74 4 , , PUNCT ejpam-2219 74 5 j.f.alzaidy j.f.alzaidy ADJ ejpam-2219 74 6 / / SYM ejpam-2219 74 7 eur eur PROPN ejpam-2219 74 8 . . PUNCT ejpam-2219 75 1 j. j. PROPN ejpam-2219 75 2 pure pure PROPN ejpam-2219 75 3 appl appl PROPN ejpam-2219 75 4 . . PROPN ejpam-2219 75 5 math math PROPN ejpam-2219 75 6 , , PUNCT ejpam-2219 75 7 10 10 NUM ejpam-2219 75 8 ( ( PUNCT ejpam-2219 75 9 3 3 NUM ejpam-2219 75 10 ) ) PUNCT ejpam-2219 75 11 ( ( PUNCT ejpam-2219 75 12 2017 2017 NUM ejpam-2219 75 13 ) ) PUNCT ejpam-2219 75 14 , , PUNCT ejpam-2219 75 15 563 563 NUM ejpam-2219 75 16 - - SYM ejpam-2219 75 17 573 573 NUM ejpam-2219 75 18 567 567 NUM ejpam-2219 75 19 3 3 NUM ejpam-2219 75 20 . . PUNCT ejpam-2219 76 1 the the DET ejpam-2219 76 2 bts bt NOUN ejpam-2219 76 3 and and CCONJ ejpam-2219 76 4 exact exact ADJ ejpam-2219 76 5 solution solution NOUN ejpam-2219 76 6 for for ADP ejpam-2219 76 7 cgl cgl NOUN ejpam-2219 76 8 equation equation NOUN ejpam-2219 76 9 we we PRON ejpam-2219 76 10 recall recall VERB ejpam-2219 76 11 the the DET ejpam-2219 76 12 definition definition NOUN ejpam-2219 76 13 [ [ X ejpam-2219 76 14 14 14 NUM ejpam-2219 76 15 , , PUNCT ejpam-2219 76 16 3 3 NUM ejpam-2219 76 17 ] ] PUNCT ejpam-2219 76 18 of of ADP ejpam-2219 76 19 a a DET ejpam-2219 76 20 differential differential ADJ ejpam-2219 76 21 equation equation NOUN ejpam-2219 76 22 ( ( PUNCT ejpam-2219 76 23 de de NOUN ejpam-2219 76 24 ) ) PUNCT ejpam-2219 76 25 that that PRON ejpam-2219 76 26 describes describe VERB ejpam-2219 76 27 a a DET ejpam-2219 76 28 pss pss PROPN ejpam-2219 76 29 . . PUNCT ejpam-2219 77 1 let let VERB ejpam-2219 77 2 m2 m2 PROPN ejpam-2219 77 3 be be AUX ejpam-2219 77 4 a a DET ejpam-2219 77 5 two two NUM ejpam-2219 77 6 dimensional dimensional ADJ ejpam-2219 77 7 differentiable differentiable NOUN ejpam-2219 77 8 manifold manifold NOUN ejpam-2219 77 9 with with ADP ejpam-2219 77 10 coordinates coordinate NOUN ejpam-2219 77 11 ( ( PUNCT ejpam-2219 77 12 x x X ejpam-2219 77 13 , , PUNCT ejpam-2219 77 14 t t PROPN ejpam-2219 77 15 ) ) PUNCT ejpam-2219 77 16 . . PUNCT ejpam-2219 78 1 a a DET ejpam-2219 78 2 de de X ejpam-2219 78 3 for for ADP ejpam-2219 78 4 a a DET ejpam-2219 78 5 real real ADJ ejpam-2219 78 6 function function NOUN ejpam-2219 78 7 u(x u(x NOUN ejpam-2219 78 8 , , PUNCT ejpam-2219 78 9 t t PROPN ejpam-2219 78 10 ) ) PUNCT ejpam-2219 78 11 describes describe VERB ejpam-2219 78 12 a a DET ejpam-2219 78 13 pss pss PROPN ejpam-2219 78 14 if if SCONJ ejpam-2219 78 15 it it PRON ejpam-2219 78 16 is be AUX ejpam-2219 78 17 a a DET ejpam-2219 78 18 necessary necessary ADJ ejpam-2219 78 19 and and CCONJ ejpam-2219 78 20 sufficient sufficient ADJ ejpam-2219 78 21 condition condition NOUN ejpam-2219 78 22 for for ADP ejpam-2219 78 23 the the DET ejpam-2219 78 24 existence existence NOUN ejpam-2219 78 25 of of ADP ejpam-2219 78 26 differentiable differentiable ADJ ejpam-2219 78 27 functions function NOUN ejpam-2219 78 28 fij fij PROPN ejpam-2219 78 29 , , PUNCT ejpam-2219 78 30 1 1 NUM ejpam-2219 78 31 ≤ ≤ NUM ejpam-2219 78 32 i i X ejpam-2219 78 33 ≤ ≤ NOUN ejpam-2219 78 34 3 3 NUM ejpam-2219 78 35 , , PUNCT ejpam-2219 78 36 1 1 NUM ejpam-2219 78 37 ≤ ≤ NUM ejpam-2219 79 1 j j PROPN ejpam-2219 79 2 ≤ ≤ ADV ejpam-2219 79 3 2 2 NUM ejpam-2219 79 4 , , PUNCT ejpam-2219 79 5 ( ( PUNCT ejpam-2219 79 6 24 24 NUM ejpam-2219 79 7 ) ) PUNCT ejpam-2219 79 8 depending depend VERB ejpam-2219 79 9 on on ADP ejpam-2219 79 10 u u NOUN ejpam-2219 79 11 and and CCONJ ejpam-2219 79 12 its its PRON ejpam-2219 79 13 derivatives derivative NOUN ejpam-2219 79 14 such such ADJ ejpam-2219 79 15 that that SCONJ ejpam-2219 79 16 the the DET ejpam-2219 79 17 one one NUM ejpam-2219 79 18 - - PUNCT ejpam-2219 79 19 forms form NOUN ejpam-2219 79 20 ω1 ω1 PROPN ejpam-2219 79 21 = = PUNCT ejpam-2219 79 22 f11dx+ f11dx+ PROPN ejpam-2219 79 23 f12dt f12dt PROPN ejpam-2219 79 24 , , PUNCT ejpam-2219 79 25 ω2 ω2 NOUN ejpam-2219 79 26 = = SYM ejpam-2219 79 27 f21dx+ f21dx+ PROPN ejpam-2219 79 28 f22dt f22dt NUM ejpam-2219 79 29 , , PUNCT ejpam-2219 79 30 ω3 ω3 NOUN ejpam-2219 79 31 = = PUNCT ejpam-2219 79 32 f31dx+ f31dx+ PROPN ejpam-2219 79 33 f32dt f32dt PROPN ejpam-2219 79 34 , , PUNCT ejpam-2219 79 35 ( ( PUNCT ejpam-2219 79 36 25 25 NUM ejpam-2219 79 37 ) ) PUNCT ejpam-2219 79 38 satisfy satisfy VERB ejpam-2219 79 39 the the DET ejpam-2219 79 40 structure structure NOUN ejpam-2219 79 41 equations equation NOUN ejpam-2219 79 42 of of ADP ejpam-2219 79 43 a a DET ejpam-2219 79 44 pss pss PROPN ejpam-2219 79 45 , , PUNCT ejpam-2219 79 46 i.e. i.e. X ejpam-2219 79 47 , , PUNCT ejpam-2219 79 48 dω1 dω1 PROPN ejpam-2219 79 49 = = SYM ejpam-2219 79 50 ω3 ω3 PROPN ejpam-2219 79 51 ∧ ∧ PROPN ejpam-2219 79 52 ω2 ω2 PROPN ejpam-2219 79 53 , , PUNCT ejpam-2219 79 54 dω2 dω2 X ejpam-2219 79 55 = = SYM ejpam-2219 79 56 ω1 ω1 PROPN ejpam-2219 79 57 ∧ ∧ PROPN ejpam-2219 79 58 ω3 ω3 PROPN ejpam-2219 79 59 , , PUNCT ejpam-2219 79 60 dω3 dω3 NOUN ejpam-2219 79 61 = = SYM ejpam-2219 79 62 ω1 ω1 PROPN ejpam-2219 79 63 ∧ ∧ PROPN ejpam-2219 79 64 ω2 ω2 PROPN ejpam-2219 79 65 . . PUNCT ejpam-2219 80 1 ( ( PUNCT ejpam-2219 80 2 26 26 NUM ejpam-2219 80 3 ) ) PUNCT ejpam-2219 80 4 as as ADP ejpam-2219 80 5 a a DET ejpam-2219 80 6 consequence consequence NOUN ejpam-2219 80 7 , , PUNCT ejpam-2219 80 8 each each DET ejpam-2219 80 9 solution solution NOUN ejpam-2219 80 10 of of ADP ejpam-2219 80 11 the the DET ejpam-2219 80 12 de de X ejpam-2219 80 13 provides provide VERB ejpam-2219 80 14 a a DET ejpam-2219 80 15 local local ADJ ejpam-2219 80 16 metric metric NOUN ejpam-2219 80 17 on on ADP ejpam-2219 80 18 m2 m2 PROPN ejpam-2219 80 19 , , PUNCT ejpam-2219 80 20 whose whose DET ejpam-2219 80 21 gaussian gaussian ADJ ejpam-2219 80 22 curvature curvature NOUN ejpam-2219 80 23 is be AUX ejpam-2219 80 24 constant constant ADJ ejpam-2219 80 25 , , PUNCT ejpam-2219 80 26 equal equal ADJ ejpam-2219 80 27 to to ADP ejpam-2219 80 28 -1 -1 VERB ejpam-2219 80 29 . . PUNCT ejpam-2219 81 1 moreover moreover ADV ejpam-2219 81 2 , , PUNCT ejpam-2219 81 3 the the DET ejpam-2219 81 4 above above ADJ ejpam-2219 81 5 definition definition NOUN ejpam-2219 81 6 is be AUX ejpam-2219 81 7 equivalent equivalent ADJ ejpam-2219 81 8 to to ADP ejpam-2219 81 9 saying say VERB ejpam-2219 81 10 that that SCONJ ejpam-2219 81 11 de de PROPN ejpam-2219 81 12 for for ADP ejpam-2219 81 13 u u NOUN ejpam-2219 81 14 is be AUX ejpam-2219 81 15 the the DET ejpam-2219 81 16 integrability integrability NOUN ejpam-2219 81 17 condition condition NOUN ejpam-2219 81 18 for for ADP ejpam-2219 81 19 the the DET ejpam-2219 81 20 problem problem NOUN ejpam-2219 81 21 [ [ X ejpam-2219 81 22 25 25 NUM ejpam-2219 81 23 , , PUNCT ejpam-2219 81 24 4 4 NUM ejpam-2219 81 25 ] ] PUNCT ejpam-2219 81 26 : : PUNCT ejpam-2219 81 27 dφ dφ ADP ejpam-2219 81 28 = = SYM ejpam-2219 81 29 ωφ ωφ PROPN ejpam-2219 81 30 , , PUNCT ejpam-2219 81 31 φ φ NOUN ejpam-2219 81 32 = = SYM ejpam-2219 81 33 ( ( PUNCT ejpam-2219 81 34 φ1 φ1 PROPN ejpam-2219 81 35 φ2 φ2 PROPN ejpam-2219 81 36 ) ) PUNCT ejpam-2219 81 37 , , PUNCT ejpam-2219 81 38 ( ( PUNCT ejpam-2219 81 39 27 27 NUM ejpam-2219 81 40 ) ) PUNCT ejpam-2219 81 41 where where SCONJ ejpam-2219 81 42 d d PROPN ejpam-2219 81 43 denotes denote VERB ejpam-2219 81 44 exterior exterior ADJ ejpam-2219 81 45 differentiation differentiation NOUN ejpam-2219 81 46 , , PUNCT ejpam-2219 81 47 φ φ PROPN ejpam-2219 81 48 is be AUX ejpam-2219 81 49 a a DET ejpam-2219 81 50 column column NOUN ejpam-2219 81 51 vector vector NOUN ejpam-2219 81 52 and and CCONJ ejpam-2219 81 53 the the DET ejpam-2219 81 54 2 2 NUM ejpam-2219 81 55 × × NOUN ejpam-2219 81 56 2 2 NUM ejpam-2219 81 57 matrix matrix NOUN ejpam-2219 81 58 ω ω NOUN ejpam-2219 81 59 ( ( PUNCT ejpam-2219 81 60 ωij ωij INTJ ejpam-2219 81 61 , , PUNCT ejpam-2219 81 62 i i PRON ejpam-2219 81 63 , , PUNCT ejpam-2219 81 64 j j PROPN ejpam-2219 81 65 = = SYM ejpam-2219 81 66 1 1 NUM ejpam-2219 81 67 , , PUNCT ejpam-2219 81 68 2 2 NUM ejpam-2219 81 69 ) ) PUNCT ejpam-2219 81 70 is be AUX ejpam-2219 81 71 traceless traceless NOUN ejpam-2219 81 72 ω ω NOUN ejpam-2219 82 1 = = SYM ejpam-2219 82 2 1 1 NUM ejpam-2219 82 3 2 2 NUM ejpam-2219 82 4 ( ( PUNCT ejpam-2219 82 5 ω2 ω2 ADJ ejpam-2219 82 6 ω1 ω1 PROPN ejpam-2219 82 7 − − PROPN ejpam-2219 82 8 ω3 ω3 PROPN ejpam-2219 82 9 ω1 ω1 PROPN ejpam-2219 82 10 + + CCONJ ejpam-2219 82 11 ω3 ω3 NOUN ejpam-2219 82 12 −ω2 −ω2 NOUN ejpam-2219 82 13 ) ) PUNCT ejpam-2219 82 14 . . PUNCT ejpam-2219 83 1 take take VERB ejpam-2219 83 2 ω ω NOUN ejpam-2219 83 3 = = PUNCT ejpam-2219 83 4 ( ( PUNCT ejpam-2219 83 5 ηdx+adt ηdx+adt NOUN ejpam-2219 83 6 qdx+bdt qdx+bdt NOUN ejpam-2219 83 7 rdx+ rdx+ NOUN ejpam-2219 83 8 cdt cdt PROPN ejpam-2219 83 9 −ηdx−adt −ηdx−adt NOUN ejpam-2219 83 10 ) ) PUNCT ejpam-2219 83 11 = = SYM ejpam-2219 83 12 sdx+ sdx+ PROPN ejpam-2219 83 13 tdt tdt PROPN ejpam-2219 83 14 , , PUNCT ejpam-2219 83 15 ( ( PUNCT ejpam-2219 83 16 28 28 NUM ejpam-2219 83 17 ) ) PUNCT ejpam-2219 83 18 from from ADP ejpam-2219 83 19 eqs eqs PROPN ejpam-2219 83 20 . . PUNCT ejpam-2219 84 1 ( ( PUNCT ejpam-2219 84 2 27 27 NUM ejpam-2219 84 3 ) ) PUNCT ejpam-2219 84 4 and and CCONJ ejpam-2219 84 5 ( ( PUNCT ejpam-2219 84 6 28 28 NUM ejpam-2219 84 7 ) ) PUNCT ejpam-2219 84 8 , , PUNCT ejpam-2219 84 9 we we PRON ejpam-2219 84 10 obtain obtain VERB ejpam-2219 84 11 φx φx ADV ejpam-2219 84 12 = = SYM ejpam-2219 84 13 sφ sφ PROPN ejpam-2219 84 14 , , PUNCT ejpam-2219 84 15 φt φt NOUN ejpam-2219 84 16 = = SYM ejpam-2219 84 17 tφ tφ PROPN ejpam-2219 84 18 , , PUNCT ejpam-2219 84 19 ( ( PUNCT ejpam-2219 84 20 29 29 NUM ejpam-2219 84 21 ) ) PUNCT ejpam-2219 84 22 where where SCONJ ejpam-2219 84 23 s s PRON ejpam-2219 84 24 and and CCONJ ejpam-2219 84 25 t t PROPN ejpam-2219 84 26 are be AUX ejpam-2219 84 27 two two NUM ejpam-2219 84 28 2× 2× NUM ejpam-2219 84 29 2 2 NUM ejpam-2219 84 30 null null ADJ ejpam-2219 84 31 - - PUNCT ejpam-2219 84 32 trace trace NOUN ejpam-2219 84 33 matrices matrix NOUN ejpam-2219 84 34 s s PART ejpam-2219 84 35 = = PUNCT ejpam-2219 84 36 ( ( PUNCT ejpam-2219 84 37 η η X ejpam-2219 84 38 q q NOUN ejpam-2219 84 39 r r NOUN ejpam-2219 84 40 −η −η NOUN ejpam-2219 84 41 ) ) PUNCT ejpam-2219 84 42 , , PUNCT ejpam-2219 84 43 ( ( PUNCT ejpam-2219 84 44 30 30 NUM ejpam-2219 84 45 ) ) PUNCT ejpam-2219 84 46 t t NOUN ejpam-2219 85 1 = = SYM ejpam-2219 85 2 ( ( PUNCT ejpam-2219 85 3 a a DET ejpam-2219 85 4 b b X ejpam-2219 85 5 c c NOUN ejpam-2219 85 6 −a −a NOUN ejpam-2219 85 7 ) ) PUNCT ejpam-2219 85 8 . . PUNCT ejpam-2219 86 1 ( ( PUNCT ejpam-2219 86 2 31 31 NUM ejpam-2219 86 3 ) ) PUNCT ejpam-2219 86 4 a.r a.r PROPN ejpam-2219 86 5 . . PROPN ejpam-2219 86 6 shehata shehata PROPN ejpam-2219 86 7 , , PUNCT ejpam-2219 86 8 j.f.alzaidy j.f.alzaidy ADJ ejpam-2219 86 9 / / SYM ejpam-2219 86 10 eur eur PROPN ejpam-2219 86 11 . . PUNCT ejpam-2219 87 1 j. j. PROPN ejpam-2219 87 2 pure pure PROPN ejpam-2219 87 3 appl appl PROPN ejpam-2219 87 4 . . PROPN ejpam-2219 87 5 math math PROPN ejpam-2219 87 6 , , PUNCT ejpam-2219 87 7 10 10 NUM ejpam-2219 87 8 ( ( PUNCT ejpam-2219 87 9 3 3 NUM ejpam-2219 87 10 ) ) PUNCT ejpam-2219 87 11 ( ( PUNCT ejpam-2219 87 12 2017 2017 NUM ejpam-2219 87 13 ) ) PUNCT ejpam-2219 87 14 , , PUNCT ejpam-2219 87 15 563 563 NUM ejpam-2219 87 16 - - SYM ejpam-2219 87 17 573 573 NUM ejpam-2219 87 18 568 568 NUM ejpam-2219 87 19 here here ADV ejpam-2219 87 20 η η PROPN ejpam-2219 87 21 is be AUX ejpam-2219 87 22 a a DET ejpam-2219 87 23 parameter parameter NOUN ejpam-2219 87 24 , , PUNCT ejpam-2219 87 25 independent independent ADJ ejpam-2219 87 26 of of ADP ejpam-2219 87 27 x x PROPN ejpam-2219 87 28 and and CCONJ ejpam-2219 87 29 t t PROPN ejpam-2219 87 30 , , PUNCT ejpam-2219 87 31 while while SCONJ ejpam-2219 87 32 q q PRON ejpam-2219 87 33 and and CCONJ ejpam-2219 87 34 r r NOUN ejpam-2219 87 35 are be AUX ejpam-2219 87 36 functions function NOUN ejpam-2219 87 37 of of ADP ejpam-2219 87 38 x x PUNCT ejpam-2219 87 39 and and CCONJ ejpam-2219 87 40 t. t. NOUN ejpam-2219 87 41 now now ADV ejpam-2219 87 42 0 0 PUNCT ejpam-2219 88 1 = = SYM ejpam-2219 88 2 d2φ d2φ PRON ejpam-2219 88 3 = = PUNCT ejpam-2219 88 4 dωφ− dωφ− PROPN ejpam-2219 88 5 ω ω PROPN ejpam-2219 88 6 ∧ ∧ PROPN ejpam-2219 88 7 dφ dφ ADP ejpam-2219 88 8 = = PUNCT ejpam-2219 88 9 ( ( PUNCT ejpam-2219 88 10 dω− dω− PROPN ejpam-2219 88 11 ω ω NUM ejpam-2219 88 12 ∧ ∧ PROPN ejpam-2219 88 13 ω)φ ω)φ NOUN ejpam-2219 88 14 , , PUNCT ejpam-2219 88 15 which which PRON ejpam-2219 88 16 requires require VERB ejpam-2219 88 17 the the DET ejpam-2219 88 18 vanishing vanishing NOUN ejpam-2219 88 19 of of ADP ejpam-2219 88 20 the the DET ejpam-2219 88 21 two two NUM ejpam-2219 88 22 form form NOUN ejpam-2219 88 23 θ θ PROPN ejpam-2219 88 24 ≡ ≡ PROPN ejpam-2219 88 25 dω− dω− PROPN ejpam-2219 88 26 ω ω PROPN ejpam-2219 88 27 ∧ ∧ PROPN ejpam-2219 88 28 ω ω PROPN ejpam-2219 88 29 = = SYM ejpam-2219 88 30 0 0 PROPN ejpam-2219 88 31 , , PUNCT ejpam-2219 88 32 ( ( PUNCT ejpam-2219 88 33 32 32 NUM ejpam-2219 88 34 ) ) PUNCT ejpam-2219 88 35 or or CCONJ ejpam-2219 88 36 in in ADP ejpam-2219 88 37 component component NOUN ejpam-2219 88 38 form form NOUN ejpam-2219 88 39 −ax −ax NOUN ejpam-2219 88 40 + + CCONJ ejpam-2219 88 41 qc qc PROPN ejpam-2219 88 42 − − PROPN ejpam-2219 88 43 rb rb NOUN ejpam-2219 88 44 = = SYM ejpam-2219 88 45 0 0 NUM ejpam-2219 88 46 qt qt NOUN ejpam-2219 88 47 − − PROPN ejpam-2219 89 1 2aq 2aq ADJ ejpam-2219 89 2 −bx −bx NOUN ejpam-2219 90 1 + + CCONJ ejpam-2219 90 2 2ηb 2ηb ADJ ejpam-2219 90 3 = = SYM ejpam-2219 90 4 0 0 NUM ejpam-2219 90 5 rt rt PROPN ejpam-2219 91 1 − − PROPN ejpam-2219 91 2 cx cx PROPN ejpam-2219 92 1 + + CCONJ ejpam-2219 92 2 2ar 2ar ADJ ejpam-2219 92 3 − − NOUN ejpam-2219 92 4 2ηc 2ηc NOUN ejpam-2219 92 5 = = SYM ejpam-2219 92 6 0 0 X ejpam-2219 92 7 . . PUNCT ejpam-2219 93 1 ( ( PUNCT ejpam-2219 93 2 33 33 NUM ejpam-2219 93 3 ) ) PUNCT ejpam-2219 93 4 chern chern NOUN ejpam-2219 93 5 and and CCONJ ejpam-2219 93 6 tenenblat tenenblat ADJ ejpam-2219 94 1 [ [ X ejpam-2219 94 2 12 12 NUM ejpam-2219 94 3 ] ] PUNCT ejpam-2219 94 4 obtained obtain VERB ejpam-2219 94 5 eq eq ADP ejpam-2219 94 6 . . PUNCT ejpam-2219 95 1 ( ( PUNCT ejpam-2219 95 2 33 33 NUM ejpam-2219 95 3 ) ) PUNCT ejpam-2219 95 4 directly directly ADV ejpam-2219 95 5 from from ADP ejpam-2219 95 6 the the DET ejpam-2219 95 7 structure structure NOUN ejpam-2219 95 8 equations equation NOUN ejpam-2219 95 9 ( ( PUNCT ejpam-2219 95 10 26 26 NUM ejpam-2219 95 11 ) ) PUNCT ejpam-2219 95 12 . . PUNCT ejpam-2219 96 1 by by ADP ejpam-2219 96 2 suitably suitably ADV ejpam-2219 96 3 choosing choose VERB ejpam-2219 96 4 r r NOUN ejpam-2219 96 5 , , PUNCT ejpam-2219 96 6 a a DET ejpam-2219 96 7 , , PUNCT ejpam-2219 96 8 b b NOUN ejpam-2219 96 9 and and CCONJ ejpam-2219 96 10 c c PROPN ejpam-2219 96 11 in in ADP ejpam-2219 96 12 ( ( PUNCT ejpam-2219 96 13 33 33 NUM ejpam-2219 96 14 ) ) PUNCT ejpam-2219 96 15 , , PUNCT ejpam-2219 96 16 we we PRON ejpam-2219 96 17 shall shall AUX ejpam-2219 96 18 obtain obtain VERB ejpam-2219 96 19 various various ADJ ejpam-2219 96 20 cgl cgl ADJ ejpam-2219 96 21 equation equation NOUN ejpam-2219 96 22 which which PRON ejpam-2219 96 23 q q NOUN ejpam-2219 96 24 must must AUX ejpam-2219 96 25 satisfy satisfy VERB ejpam-2219 96 26 . . PUNCT ejpam-2219 97 1 konno konno NOUN ejpam-2219 97 2 and and CCONJ ejpam-2219 97 3 wadati wadati PROPN ejpam-2219 97 4 introduced introduce VERB ejpam-2219 97 5 the the DET ejpam-2219 97 6 function function NOUN ejpam-2219 97 7 [ [ X ejpam-2219 97 8 23 23 NUM ejpam-2219 97 9 ] ] X ejpam-2219 97 10 γ γ PROPN ejpam-2219 97 11 = = SYM ejpam-2219 97 12 φ1 φ1 PROPN ejpam-2219 97 13 φ2 φ2 PROPN ejpam-2219 97 14 , , PUNCT ejpam-2219 97 15 ( ( PUNCT ejpam-2219 97 16 34 34 NUM ejpam-2219 97 17 ) ) PUNCT ejpam-2219 97 18 this this DET ejpam-2219 97 19 function function NOUN ejpam-2219 97 20 first first ADV ejpam-2219 97 21 appeared appear VERB ejpam-2219 97 22 used use VERB ejpam-2219 97 23 and and CCONJ ejpam-2219 97 24 explained explain VERB ejpam-2219 97 25 in in ADP ejpam-2219 97 26 the the DET ejpam-2219 97 27 geometric geometric ADJ ejpam-2219 97 28 context context NOUN ejpam-2219 97 29 of of ADP ejpam-2219 97 30 pss pss PROPN ejpam-2219 97 31 equations equation NOUN ejpam-2219 97 32 in in ADP ejpam-2219 97 33 [ [ X ejpam-2219 97 34 10 10 NUM ejpam-2219 97 35 , , PUNCT ejpam-2219 97 36 24 24 NUM ejpam-2219 97 37 ] ] PUNCT ejpam-2219 97 38 , , PUNCT ejpam-2219 97 39 and and CCONJ ejpam-2219 97 40 see see VERB ejpam-2219 97 41 also also ADV ejpam-2219 97 42 the the DET ejpam-2219 97 43 classical classical ADJ ejpam-2219 97 44 papers paper NOUN ejpam-2219 97 45 by by ADP ejpam-2219 97 46 sasaki sasaki PROPN ejpam-2219 98 1 [ [ X ejpam-2219 98 2 26 26 NUM ejpam-2219 98 3 ] ] PUNCT ejpam-2219 98 4 and and CCONJ ejpam-2219 98 5 chern chern NOUN ejpam-2219 98 6 - - PUNCT ejpam-2219 98 7 tenenblat tenenblat NOUN ejpam-2219 98 8 [ [ X ejpam-2219 98 9 12 12 NUM ejpam-2219 98 10 ] ] PUNCT ejpam-2219 98 11 . . PUNCT ejpam-2219 99 1 then then ADV ejpam-2219 99 2 eq eq X ejpam-2219 99 3 . . PUNCT ejpam-2219 100 1 ( ( PUNCT ejpam-2219 100 2 29 29 NUM ejpam-2219 100 3 ) ) PUNCT ejpam-2219 100 4 is be AUX ejpam-2219 100 5 reduced reduce VERB ejpam-2219 100 6 to to ADP ejpam-2219 100 7 the the DET ejpam-2219 100 8 riccati riccati PROPN ejpam-2219 100 9 equations equation NOUN ejpam-2219 100 10 : : PUNCT ejpam-2219 101 1 ∂γ ∂γ PROPN ejpam-2219 101 2 ∂x ∂x PROPN ejpam-2219 101 3 = = SYM ejpam-2219 101 4 ηγ− ηγ− NOUN ejpam-2219 101 5 rγ2 rγ2 NOUN ejpam-2219 102 1 + + X ejpam-2219 102 2 q q ADJ ejpam-2219 102 3 , , PUNCT ejpam-2219 102 4 ( ( PUNCT ejpam-2219 102 5 35 35 NUM ejpam-2219 102 6 ) ) PUNCT ejpam-2219 102 7 ∂γ ∂γ PROPN ejpam-2219 102 8 ∂t ∂t PROPN ejpam-2219 102 9 = = PUNCT ejpam-2219 102 10 2aγ− 2aγ− NUM ejpam-2219 102 11 cγ2 cγ2 PROPN ejpam-2219 102 12 + + PROPN ejpam-2219 102 13 b. b. PROPN ejpam-2219 102 14 ( ( PUNCT ejpam-2219 102 15 36 36 NUM ejpam-2219 102 16 ) ) PUNCT ejpam-2219 102 17 our our PRON ejpam-2219 102 18 procedure procedure NOUN ejpam-2219 102 19 in in ADP ejpam-2219 102 20 the the DET ejpam-2219 102 21 following following NOUN ejpam-2219 102 22 is be AUX ejpam-2219 102 23 that that SCONJ ejpam-2219 102 24 we we PRON ejpam-2219 102 25 construct construct VERB ejpam-2219 102 26 a a DET ejpam-2219 102 27 transformation transformation NOUN ejpam-2219 102 28 γ′ γ′ VERB ejpam-2219 102 29 satisfying satisfy VERB ejpam-2219 102 30 the the DET ejpam-2219 102 31 same same ADJ ejpam-2219 102 32 equation equation NOUN ejpam-2219 102 33 as as ADP ejpam-2219 102 34 ( ( PUNCT ejpam-2219 102 35 35 35 NUM ejpam-2219 102 36 ) ) PUNCT ejpam-2219 102 37 and and CCONJ ejpam-2219 102 38 ( ( PUNCT ejpam-2219 102 39 36 36 NUM ejpam-2219 102 40 ) ) PUNCT ejpam-2219 102 41 with with ADP ejpam-2219 102 42 a a DET ejpam-2219 102 43 potential potential ADJ ejpam-2219 102 44 u′ u′ PROPN ejpam-2219 102 45 where where SCONJ ejpam-2219 102 46 u′ u′ PROPN ejpam-2219 102 47 = = SYM ejpam-2219 102 48 u+ u+ NOUN ejpam-2219 102 49 f(γ f(γ PROPN ejpam-2219 102 50 , , PUNCT ejpam-2219 102 51 η η NOUN ejpam-2219 102 52 ) ) PUNCT ejpam-2219 102 53 , , PUNCT ejpam-2219 102 54 ( ( PUNCT ejpam-2219 102 55 37 37 NUM ejpam-2219 102 56 ) ) PUNCT ejpam-2219 102 57 chern chern NOUN ejpam-2219 102 58 and and CCONJ ejpam-2219 102 59 tenenblat tenenblat ADJ ejpam-2219 103 1 [ [ X ejpam-2219 103 2 12 12 NUM ejpam-2219 103 3 ] ] PUNCT ejpam-2219 103 4 introduced introduce VERB ejpam-2219 103 5 several several ADJ ejpam-2219 103 6 examples example NOUN ejpam-2219 103 7 of of ADP ejpam-2219 103 8 ( ( PUNCT ejpam-2219 103 9 37 37 NUM ejpam-2219 103 10 ) ) PUNCT ejpam-2219 103 11 for for ADP ejpam-2219 103 12 pss pss PROPN ejpam-2219 103 13 equations equation NOUN ejpam-2219 103 14 . . PUNCT ejpam-2219 104 1 for for ADP ejpam-2219 104 2 use use NOUN ejpam-2219 104 3 in in ADP ejpam-2219 104 4 the the DET ejpam-2219 104 5 sequel sequel NOUN ejpam-2219 104 6 , , PUNCT ejpam-2219 104 7 we we PRON ejpam-2219 104 8 list list VERB ejpam-2219 104 9 the the DET ejpam-2219 104 10 cgl cgl PROPN ejpam-2219 104 11 equation equation NOUN ejpam-2219 104 12 and and CCONJ ejpam-2219 104 13 their their PRON ejpam-2219 104 14 corresponding correspond VERB ejpam-2219 104 15 bt bt NOUN ejpam-2219 104 16 in in ADP ejpam-2219 104 17 the the DET ejpam-2219 104 18 following following NOUN ejpam-2219 104 19 . . PUNCT ejpam-2219 105 1 the the DET ejpam-2219 105 2 cgl cgl PROPN ejpam-2219 105 3 equation equation NOUN ejpam-2219 105 4 for for ADP ejpam-2219 105 5 any any DET ejpam-2219 105 6 solution solution NOUN ejpam-2219 105 7 u(x u(x NOUN ejpam-2219 105 8 , , PUNCT ejpam-2219 105 9 t t PROPN ejpam-2219 105 10 ) ) PUNCT ejpam-2219 105 11 of of ADP ejpam-2219 105 12 the the DET ejpam-2219 105 13 cgl cgl PROPN ejpam-2219 105 14 equation equation NOUN ejpam-2219 105 15 ( ( PUNCT ejpam-2219 105 16 23 23 NUM ejpam-2219 105 17 ) ) PUNCT ejpam-2219 105 18 , , PUNCT ejpam-2219 105 19 the the DET ejpam-2219 105 20 matrices matrix NOUN ejpam-2219 105 21 s s PART ejpam-2219 105 22 and and CCONJ ejpam-2219 105 23 t t PROPN ejpam-2219 105 24 are be AUX ejpam-2219 105 25 s s NOUN ejpam-2219 105 26 = = PUNCT ejpam-2219 105 27 ( ( PUNCT ejpam-2219 105 28 η η X ejpam-2219 105 29 ue−iµt ue−iµt X ejpam-2219 105 30 −u∗eiµt −u∗eiµt X ejpam-2219 105 31 −η −η NOUN ejpam-2219 105 32 ) ) PUNCT ejpam-2219 105 33 , , PUNCT ejpam-2219 105 34 ( ( PUNCT ejpam-2219 105 35 38 38 NUM ejpam-2219 105 36 ) ) PUNCT ejpam-2219 105 37 t t NOUN ejpam-2219 105 38 = = SYM ejpam-2219 105 39 ( ( PUNCT ejpam-2219 105 40 2iη2a+ 2iη2a+ NUM ejpam-2219 105 41 ia|u|2 ia|u|2 PROPN ejpam-2219 105 42 ( ( PUNCT ejpam-2219 105 43 2iηau+ 2iηau+ NUM ejpam-2219 105 44 aiux)e−iµt aiux)e−iµt X ejpam-2219 105 45 ( ( PUNCT ejpam-2219 105 46 −2iηau∗ −2iηau∗ X ejpam-2219 105 47 + + CCONJ ejpam-2219 105 48 aiu∗x)eiµt aiu∗x)eiµt PROPN ejpam-2219 105 49 −2iη2a− −2iη2a− VERB ejpam-2219 105 50 ia|u|2 ia|u|2 PROPN ejpam-2219 105 51 ) ) PUNCT ejpam-2219 105 52 , , PUNCT ejpam-2219 105 53 ( ( PUNCT ejpam-2219 105 54 39 39 NUM ejpam-2219 105 55 ) ) PUNCT ejpam-2219 105 56 a.r a.r PROPN ejpam-2219 105 57 . . PROPN ejpam-2219 105 58 shehata shehata PROPN ejpam-2219 105 59 , , PUNCT ejpam-2219 105 60 j.f.alzaidy j.f.alzaidy ADJ ejpam-2219 105 61 / / SYM ejpam-2219 105 62 eur eur PROPN ejpam-2219 105 63 . . PUNCT ejpam-2219 106 1 j. j. PROPN ejpam-2219 106 2 pure pure PROPN ejpam-2219 106 3 appl appl PROPN ejpam-2219 106 4 . . PROPN ejpam-2219 106 5 math math PROPN ejpam-2219 106 6 , , PUNCT ejpam-2219 106 7 10 10 NUM ejpam-2219 106 8 ( ( PUNCT ejpam-2219 106 9 3 3 NUM ejpam-2219 106 10 ) ) PUNCT ejpam-2219 106 11 ( ( PUNCT ejpam-2219 106 12 2017 2017 NUM ejpam-2219 106 13 ) ) PUNCT ejpam-2219 106 14 , , PUNCT ejpam-2219 106 15 563 563 NUM ejpam-2219 106 16 - - SYM ejpam-2219 106 17 573 573 NUM ejpam-2219 106 18 569 569 NUM ejpam-2219 106 19 the the DET ejpam-2219 106 20 above above ADJ ejpam-2219 106 21 matrices matrix NOUN ejpam-2219 106 22 s s PROPN ejpam-2219 106 23 , , PUNCT ejpam-2219 106 24 t t PROPN ejpam-2219 106 25 satisfy satisfy PROPN ejpam-2219 106 26 eqs eqs PROPN ejpam-2219 106 27 . . PUNCT ejpam-2219 107 1 ( ( PUNCT ejpam-2219 107 2 33 33 NUM ejpam-2219 107 3 ) ) PUNCT ejpam-2219 107 4 . . PUNCT ejpam-2219 108 1 then then ADV ejpam-2219 108 2 eq eq X ejpam-2219 108 3 . . PUNCT ejpam-2219 109 1 ( ( PUNCT ejpam-2219 109 2 35 35 NUM ejpam-2219 109 3 ) ) PUNCT ejpam-2219 109 4 becomes become VERB ejpam-2219 110 1 ∂γ ∂γ PROPN ejpam-2219 110 2 ∂x ∂x PROPN ejpam-2219 110 3 = = PUNCT ejpam-2219 110 4 ηγ ηγ PROPN ejpam-2219 110 5 + + NUM ejpam-2219 110 6 ue−iµt ue−iµt NOUN ejpam-2219 110 7 + + CCONJ ejpam-2219 110 8 u∗eiµtγ2 u∗eiµtγ2 NOUN ejpam-2219 110 9 . . PUNCT ejpam-2219 111 1 ( ( PUNCT ejpam-2219 111 2 40 40 NUM ejpam-2219 111 3 ) ) PUNCT ejpam-2219 111 4 if if SCONJ ejpam-2219 111 5 we we PRON ejpam-2219 111 6 choose choose VERB ejpam-2219 111 7 γ′ γ′ PROPN ejpam-2219 111 8 and and CCONJ ejpam-2219 111 9 u′ u′ PROPN ejpam-2219 111 10 as as ADP ejpam-2219 111 11 [ [ X ejpam-2219 111 12 3 3 NUM ejpam-2219 111 13 ] ] PUNCT ejpam-2219 111 14 γ′ γ′ X ejpam-2219 111 15 = = SYM ejpam-2219 111 16 1 1 NUM ejpam-2219 111 17 γ∗ γ∗ NOUN ejpam-2219 111 18 , , PUNCT ejpam-2219 111 19 ( ( PUNCT ejpam-2219 111 20 41 41 NUM ejpam-2219 111 21 ) ) PUNCT ejpam-2219 111 22 u′ u′ PROPN ejpam-2219 111 23 = = SYM ejpam-2219 111 24 u− u− PROPN ejpam-2219 111 25 4η 4η NOUN ejpam-2219 111 26 γeiµt γeiµt VERB ejpam-2219 111 27 1 1 NUM ejpam-2219 111 28 + + CCONJ ejpam-2219 111 29 |γ|2 |γ|2 ADJ ejpam-2219 111 30 . . PUNCT ejpam-2219 112 1 ( ( PUNCT ejpam-2219 112 2 42 42 NUM ejpam-2219 112 3 ) ) PUNCT ejpam-2219 112 4 now now ADV ejpam-2219 112 5 we we PRON ejpam-2219 112 6 shall shall AUX ejpam-2219 112 7 choose choose VERB ejpam-2219 112 8 some some DET ejpam-2219 112 9 known know VERB ejpam-2219 112 10 solution solution NOUN ejpam-2219 112 11 of of ADP ejpam-2219 112 12 the the DET ejpam-2219 112 13 cgl cgl PROPN ejpam-2219 112 14 equation equation NOUN ejpam-2219 112 15 and and CCONJ ejpam-2219 112 16 substitute substitute NOUN ejpam-2219 112 17 this this DET ejpam-2219 112 18 solution solution NOUN ejpam-2219 112 19 into into ADP ejpam-2219 112 20 the the DET ejpam-2219 112 21 corresponding corresponding ADJ ejpam-2219 112 22 matrices matrix NOUN ejpam-2219 112 23 s s PART ejpam-2219 112 24 and and CCONJ ejpam-2219 112 25 t t PROPN ejpam-2219 112 26 . . PUNCT ejpam-2219 113 1 next next ADV ejpam-2219 113 2 , , PUNCT ejpam-2219 113 3 we we PRON ejpam-2219 113 4 solve solve VERB ejpam-2219 113 5 eqs eqs PROPN ejpam-2219 113 6 . . PUNCT ejpam-2219 114 1 ( ( PUNCT ejpam-2219 114 2 29 29 NUM ejpam-2219 114 3 ) ) PUNCT ejpam-2219 114 4 for for ADP ejpam-2219 114 5 φ1 φ1 NOUN ejpam-2219 114 6 and and CCONJ ejpam-2219 114 7 φ2 φ2 PROPN ejpam-2219 114 8 . . PUNCT ejpam-2219 115 1 then then ADV ejpam-2219 115 2 , , PUNCT ejpam-2219 115 3 by by ADP ejpam-2219 115 4 ( ( PUNCT ejpam-2219 115 5 34 34 NUM ejpam-2219 115 6 ) ) PUNCT ejpam-2219 115 7 and and CCONJ ejpam-2219 115 8 the the DET ejpam-2219 115 9 corresponding correspond VERB ejpam-2219 115 10 bt bt NOUN ejpam-2219 115 11 we we PRON ejpam-2219 115 12 shall shall AUX ejpam-2219 115 13 obtain obtain VERB ejpam-2219 115 14 the the DET ejpam-2219 115 15 new new ADJ ejpam-2219 115 16 solution solution NOUN ejpam-2219 115 17 for for ADP ejpam-2219 115 18 the the DET ejpam-2219 115 19 cgl cgl PROPN ejpam-2219 115 20 equation equation NOUN ejpam-2219 115 21 . . PUNCT ejpam-2219 116 1 substitute substitute PROPN ejpam-2219 116 2 u u PROPN ejpam-2219 116 3 = = NOUN ejpam-2219 116 4 0 0 NUM ejpam-2219 116 5 into into ADP ejpam-2219 116 6 the the DET ejpam-2219 116 7 matrices matrix NOUN ejpam-2219 116 8 s s PART ejpam-2219 116 9 and and CCONJ ejpam-2219 116 10 t t PROPN ejpam-2219 116 11 in in ADP ejpam-2219 116 12 ( ( PUNCT ejpam-2219 116 13 38 38 NUM ejpam-2219 116 14 ) ) PUNCT ejpam-2219 116 15 and and CCONJ ejpam-2219 116 16 ( ( PUNCT ejpam-2219 116 17 39 39 NUM ejpam-2219 116 18 ) ) PUNCT ejpam-2219 116 19 , , PUNCT ejpam-2219 116 20 then then ADV ejpam-2219 116 21 by by ADP ejpam-2219 116 22 ( ( PUNCT ejpam-2219 116 23 29 29 NUM ejpam-2219 116 24 ) ) PUNCT ejpam-2219 116 25 we we PRON ejpam-2219 116 26 have have VERB ejpam-2219 116 27 dφ dφ ADJ ejpam-2219 116 28 = = PUNCT ejpam-2219 116 29 φxdx+ φxdx+ PUNCT ejpam-2219 116 30 φtdt φtdt ADJ ejpam-2219 116 31 = = SYM ejpam-2219 116 32 sφdρ sφdρ ADJ ejpam-2219 116 33 , , PUNCT ejpam-2219 116 34 ( ( PUNCT ejpam-2219 116 35 43 43 NUM ejpam-2219 116 36 ) ) PUNCT ejpam-2219 116 37 where where SCONJ ejpam-2219 116 38 s s VERB ejpam-2219 116 39 = = SYM ejpam-2219 116 40 ( ( PUNCT ejpam-2219 116 41 η η PROPN ejpam-2219 116 42 0 0 NUM ejpam-2219 116 43 0 0 NUM ejpam-2219 116 44 −η −η NOUN ejpam-2219 116 45 ) ) PUNCT ejpam-2219 116 46 , , PUNCT ejpam-2219 116 47 ( ( PUNCT ejpam-2219 116 48 44 44 NUM ejpam-2219 116 49 ) ) PUNCT ejpam-2219 116 50 ρ ρ PROPN ejpam-2219 116 51 = = SYM ejpam-2219 116 52 x+ x+ PROPN ejpam-2219 116 53 bt bt PROPN ejpam-2219 116 54 , , PUNCT ejpam-2219 116 55 b b NOUN ejpam-2219 116 56 = = SYM ejpam-2219 116 57 2iaη 2iaη NOUN ejpam-2219 116 58 . . PUNCT ejpam-2219 117 1 ( ( PUNCT ejpam-2219 117 2 45 45 NUM ejpam-2219 117 3 ) ) PUNCT ejpam-2219 117 4 the the DET ejpam-2219 117 5 solution solution NOUN ejpam-2219 117 6 of of ADP ejpam-2219 117 7 eq eq PROPN ejpam-2219 117 8 . . PUNCT ejpam-2219 118 1 ( ( PUNCT ejpam-2219 118 2 43 43 NUM ejpam-2219 118 3 ) ) PUNCT ejpam-2219 118 4 is be AUX ejpam-2219 118 5 φ φ NOUN ejpam-2219 118 6 = = SYM ejpam-2219 118 7 esρφ0 esρφ0 NOUN ejpam-2219 119 1 = = PUNCT ejpam-2219 119 2 ( ( PUNCT ejpam-2219 119 3 1 1 NUM ejpam-2219 119 4 + + CCONJ ejpam-2219 119 5 ρs ρs ADV ejpam-2219 119 6 + + CCONJ ejpam-2219 119 7 ρ2s2 ρ2s2 NOUN ejpam-2219 119 8 2 2 NUM ejpam-2219 119 9 ! ! PUNCT ejpam-2219 120 1 + + NUM ejpam-2219 120 2 ρ3s3 ρ3s3 NOUN ejpam-2219 120 3 3 3 X ejpam-2219 120 4 ! ! PUNCT ejpam-2219 120 5 + + CCONJ ejpam-2219 121 1 · · PUNCT ejpam-2219 121 2 · · PUNCT ejpam-2219 121 3 · · PUNCT ejpam-2219 121 4 ) ) PUNCT ejpam-2219 121 5 φ0 φ0 PROPN ejpam-2219 121 6 , , PUNCT ejpam-2219 121 7 ( ( PUNCT ejpam-2219 121 8 46 46 NUM ejpam-2219 121 9 ) ) PUNCT ejpam-2219 121 10 where where SCONJ ejpam-2219 121 11 φ0 φ0 PROPN ejpam-2219 121 12 is be AUX ejpam-2219 121 13 a a DET ejpam-2219 121 14 constant constant ADJ ejpam-2219 121 15 column column NOUN ejpam-2219 121 16 vector vector NOUN ejpam-2219 121 17 . . PUNCT ejpam-2219 122 1 the the DET ejpam-2219 122 2 solution solution NOUN ejpam-2219 122 3 of of ADP ejpam-2219 122 4 eq eq PROPN ejpam-2219 122 5 . . PUNCT ejpam-2219 123 1 ( ( PUNCT ejpam-2219 123 2 46 46 NUM ejpam-2219 123 3 ) ) PUNCT ejpam-2219 123 4 is be AUX ejpam-2219 123 5 φ φ PROPN ejpam-2219 123 6 = = PUNCT ejpam-2219 123 7 ( ( PUNCT ejpam-2219 123 8 cosh cosh PROPN ejpam-2219 123 9 ηρ+ ηρ+ NOUN ejpam-2219 123 10 sinh sinh NOUN ejpam-2219 123 11 ηρ ηρ PROPN ejpam-2219 123 12 0 0 NUM ejpam-2219 123 13 0 0 NUM ejpam-2219 123 14 cosh cosh PROPN ejpam-2219 123 15 ηρ− ηρ− PROPN ejpam-2219 123 16 sinh sinh NOUN ejpam-2219 123 17 ηρ ηρ PROPN ejpam-2219 123 18 ) ) PUNCT ejpam-2219 123 19 φ0 φ0 PROPN ejpam-2219 123 20 . . PUNCT ejpam-2219 124 1 ( ( PUNCT ejpam-2219 124 2 47 47 NUM ejpam-2219 124 3 ) ) PUNCT ejpam-2219 124 4 now now ADV ejpam-2219 124 5 , , PUNCT ejpam-2219 124 6 we we PRON ejpam-2219 124 7 choose choose VERB ejpam-2219 124 8 φ0 φ0 PROPN ejpam-2219 124 9 = = SYM ejpam-2219 124 10 ( ( PUNCT ejpam-2219 124 11 1 1 NUM ejpam-2219 124 12 , , PUNCT ejpam-2219 124 13 1)t 1)t PROPN ejpam-2219 124 14 in in ADP ejpam-2219 124 15 ( ( PUNCT ejpam-2219 124 16 47 47 NUM ejpam-2219 124 17 ) ) PUNCT ejpam-2219 124 18 , , PUNCT ejpam-2219 124 19 then then ADV ejpam-2219 124 20 we we PRON ejpam-2219 124 21 have have VERB ejpam-2219 124 22 φ φ PROPN ejpam-2219 124 23 = = SYM ejpam-2219 124 24 ( ( PUNCT ejpam-2219 124 25 eηρ eηρ ADJ ejpam-2219 124 26 e−ηρ e−ηρ NOUN ejpam-2219 124 27 ) ) PUNCT ejpam-2219 124 28 . . PUNCT ejpam-2219 125 1 ( ( PUNCT ejpam-2219 125 2 48 48 NUM ejpam-2219 125 3 ) ) PUNCT ejpam-2219 125 4 substitute substitute NOUN ejpam-2219 125 5 ( ( PUNCT ejpam-2219 125 6 48 48 NUM ejpam-2219 125 7 ) ) PUNCT ejpam-2219 125 8 into into ADP ejpam-2219 125 9 ( ( PUNCT ejpam-2219 125 10 34 34 NUM ejpam-2219 125 11 ) ) PUNCT ejpam-2219 125 12 , , PUNCT ejpam-2219 125 13 then then ADV ejpam-2219 125 14 by by ADP ejpam-2219 125 15 ( ( PUNCT ejpam-2219 125 16 42 42 NUM ejpam-2219 125 17 ) ) PUNCT ejpam-2219 125 18 , , PUNCT ejpam-2219 125 19 we we PRON ejpam-2219 125 20 obtain obtain VERB ejpam-2219 125 21 the the DET ejpam-2219 125 22 new new ADJ ejpam-2219 125 23 solutions solution NOUN ejpam-2219 125 24 of of ADP ejpam-2219 125 25 the the DET ejpam-2219 125 26 cgl cgl PROPN ejpam-2219 125 27 equation(23 equation(23 NOUN ejpam-2219 125 28 ) ) PUNCT ejpam-2219 125 29 u′ u′ X ejpam-2219 126 1 = = SYM ejpam-2219 126 2 −2ηei(2aη −2ηei(2aη NOUN ejpam-2219 126 3 2)tsech(2ηx 2)tsech(2ηx NUM ejpam-2219 126 4 ) ) PUNCT ejpam-2219 126 5 . . PUNCT ejpam-2219 127 1 ( ( PUNCT ejpam-2219 127 2 49 49 NUM ejpam-2219 127 3 ) ) PUNCT ejpam-2219 127 4 we we PRON ejpam-2219 127 5 can can AUX ejpam-2219 127 6 calculate calculate VERB ejpam-2219 127 7 the the DET ejpam-2219 127 8 gauge gauge ADJ ejpam-2219 127 9 potential potential NOUN ejpam-2219 127 10 aµ aµ PROPN ejpam-2219 127 11 and and CCONJ ejpam-2219 127 12 the the DET ejpam-2219 127 13 gauge gauge ADJ ejpam-2219 127 14 field field NOUN ejpam-2219 127 15 strengths strength NOUN ejpam-2219 127 16 fµν fµν ADJ ejpam-2219 127 17 from from ADP ejpam-2219 127 18 equations equation NOUN ejpam-2219 127 19 ( ( PUNCT ejpam-2219 127 20 6)-(10 6)-(10 NUM ejpam-2219 127 21 ) ) PUNCT ejpam-2219 127 22 and and CCONJ ejpam-2219 127 23 ( ( PUNCT ejpam-2219 127 24 20)-(22 20)-(22 NOUN ejpam-2219 127 25 ) ) PUNCT ejpam-2219 127 26 , , PUNCT ejpam-2219 127 27 then then ADV ejpam-2219 127 28 ay ay INTJ ejpam-2219 127 29 = = PUNCT ejpam-2219 127 30 ( ( PUNCT ejpam-2219 127 31 0 0 NUM ejpam-2219 127 32 −2ηea1tsech(2ηx −2ηea1tsech(2ηx NOUN ejpam-2219 127 33 ) ) PUNCT ejpam-2219 127 34 2ηe−a1tsech(2ηx 2ηe−a1tsech(2ηx NUM ejpam-2219 127 35 ) ) PUNCT ejpam-2219 127 36 0 0 NUM ejpam-2219 127 37 ) ) PUNCT ejpam-2219 127 38 , , PUNCT ejpam-2219 127 39 aȳ aȳ VERB ejpam-2219 127 40 = = SYM ejpam-2219 127 41 0 0 NUM ejpam-2219 127 42 a.r a.r PROPN ejpam-2219 127 43 . . PROPN ejpam-2219 127 44 shehata shehata PROPN ejpam-2219 127 45 , , PUNCT ejpam-2219 127 46 j.f.alzaidy j.f.alzaidy ADJ ejpam-2219 127 47 / / SYM ejpam-2219 127 48 eur eur PROPN ejpam-2219 127 49 . . PUNCT ejpam-2219 128 1 j. j. PROPN ejpam-2219 128 2 pure pure PROPN ejpam-2219 128 3 appl appl PROPN ejpam-2219 128 4 . . PROPN ejpam-2219 128 5 math math PROPN ejpam-2219 128 6 , , PUNCT ejpam-2219 128 7 10 10 NUM ejpam-2219 128 8 ( ( PUNCT ejpam-2219 128 9 3 3 NUM ejpam-2219 128 10 ) ) PUNCT ejpam-2219 128 11 ( ( PUNCT ejpam-2219 128 12 2017 2017 NUM ejpam-2219 128 13 ) ) PUNCT ejpam-2219 128 14 , , PUNCT ejpam-2219 128 15 563 563 NUM ejpam-2219 128 16 - - SYM ejpam-2219 128 17 573 573 NUM ejpam-2219 128 18 570 570 NUM ejpam-2219 128 19 ay ay NOUN ejpam-2219 128 20 = = SYM ejpam-2219 128 21 ( ( PUNCT ejpam-2219 128 22 a2 a2 PROPN ejpam-2219 128 23 b2 b2 PROPN ejpam-2219 128 24 b3 b3 PROPN ejpam-2219 128 25 −a2 −a2 PROPN ejpam-2219 128 26 ) ) PUNCT ejpam-2219 128 27 , , PUNCT ejpam-2219 128 28 az̄ az̄ ADV ejpam-2219 128 29 = = SYM ejpam-2219 128 30 ( ( PUNCT ejpam-2219 128 31 −i −i PROPN ejpam-2219 128 32 2a 2a NUM ejpam-2219 128 33 0 0 NUM ejpam-2219 128 34 0 0 PUNCT ejpam-2219 129 1 i i PRON ejpam-2219 129 2 2a 2a NUM ejpam-2219 129 3 ) ) PUNCT ejpam-2219 129 4 , , PUNCT ejpam-2219 129 5 ( ( PUNCT ejpam-2219 129 6 50 50 NUM ejpam-2219 129 7 ) ) PUNCT ejpam-2219 129 8 where where SCONJ ejpam-2219 129 9 a1 a1 NOUN ejpam-2219 129 10 = = SYM ejpam-2219 129 11 2iaη2 2iaη2 NUM ejpam-2219 129 12 , , PUNCT ejpam-2219 129 13 a2 a2 PROPN ejpam-2219 129 14 = = SYM ejpam-2219 129 15 2a1sech2(2ηx 2a1sech2(2ηx NOUN ejpam-2219 129 16 ) ) PUNCT ejpam-2219 129 17 , , PUNCT ejpam-2219 129 18 b2 b2 NOUN ejpam-2219 129 19 = = SYM ejpam-2219 129 20 2a1e 2a1e NUM ejpam-2219 129 21 a1tsech(2ηx a1tsech(2ηx NOUN ejpam-2219 129 22 ) ) PUNCT ejpam-2219 129 23 tanh(2ηx tanh(2ηx ADV ejpam-2219 129 24 ) ) PUNCT ejpam-2219 129 25 , , PUNCT ejpam-2219 129 26 b3 b3 PROPN ejpam-2219 129 27 = = SYM ejpam-2219 129 28 2a1e 2a1e NOUN ejpam-2219 129 29 −a1tsech(2ηx −a1tsech(2ηx X ejpam-2219 129 30 ) ) PUNCT ejpam-2219 129 31 tanh(2ηx tanh(2ηx ADV ejpam-2219 129 32 ) ) PUNCT ejpam-2219 129 33 . . PUNCT ejpam-2219 130 1 consequently consequently ADV ejpam-2219 130 2 , , PUNCT ejpam-2219 130 3 we we PRON ejpam-2219 130 4 obtain obtain VERB ejpam-2219 130 5 the the DET ejpam-2219 130 6 gauge gauge ADJ ejpam-2219 130 7 field field NOUN ejpam-2219 130 8 strengths strength NOUN ejpam-2219 130 9 fµν fµν ADJ ejpam-2219 130 10 as as SCONJ ejpam-2219 130 11 follows follow VERB ejpam-2219 130 12 : : PUNCT ejpam-2219 130 13 fyȳ fyȳ NOUN ejpam-2219 130 14 = = SYM ejpam-2219 130 15 −∂xay −∂xay NOUN ejpam-2219 130 16 , , PUNCT ejpam-2219 130 17 fzz̄ fzz̄ PUNCT ejpam-2219 131 1 = = PUNCT ejpam-2219 131 2 ∂taz̄ ∂taz̄ NUM ejpam-2219 131 3 − − PROPN ejpam-2219 132 1 [ [ X ejpam-2219 132 2 az az PROPN ejpam-2219 132 3 , , PUNCT ejpam-2219 132 4 az̄ az̄ PROPN ejpam-2219 132 5 ] ] PUNCT ejpam-2219 132 6 fyz fyz NOUN ejpam-2219 132 7 = = PUNCT ejpam-2219 132 8 ∂xaz ∂xaz NUM ejpam-2219 132 9 − − NOUN ejpam-2219 132 10 ∂tay ∂tay PUNCT ejpam-2219 132 11 − − PROPN ejpam-2219 133 1 [ [ X ejpam-2219 133 2 ay ay X ejpam-2219 133 3 , , PUNCT ejpam-2219 133 4 az az PROPN ejpam-2219 133 5 ] ] PUNCT ejpam-2219 133 6 , , PUNCT ejpam-2219 133 7 fȳz̄ fȳz̄ NOUN ejpam-2219 133 8 = = SYM ejpam-2219 133 9 ∂xaz̄ ∂xaz̄ PRON ejpam-2219 133 10 − − NOUN ejpam-2219 134 1 [ [ X ejpam-2219 134 2 aȳ aȳ X ejpam-2219 134 3 , , PUNCT ejpam-2219 134 4 az̄ az̄ ADV ejpam-2219 134 5 ] ] X ejpam-2219 134 6 , , PUNCT ejpam-2219 134 7 ( ( PUNCT ejpam-2219 134 8 51 51 NUM ejpam-2219 134 9 ) ) PUNCT ejpam-2219 134 10 we we PRON ejpam-2219 134 11 note note VERB ejpam-2219 134 12 that that SCONJ ejpam-2219 134 13 the the DET ejpam-2219 134 14 self self NOUN ejpam-2219 134 15 - - PUNCT ejpam-2219 134 16 dual dual ADJ ejpam-2219 134 17 su(2 su(2 NOUN ejpam-2219 134 18 ) ) PUNCT ejpam-2219 134 19 yang yang PROPN ejpam-2219 134 20 mills mills PROPN ejpam-2219 134 21 equations equations PROPN ejpam-2219 134 22 holds hold VERB ejpam-2219 134 23 . . PUNCT ejpam-2219 135 1 there there PRON ejpam-2219 135 2 are be VERB ejpam-2219 135 3 several several ADJ ejpam-2219 135 4 points point NOUN ejpam-2219 135 5 to to PART ejpam-2219 135 6 be be AUX ejpam-2219 135 7 made make VERB ejpam-2219 135 8 : : PUNCT ejpam-2219 135 9 ( ( PUNCT ejpam-2219 135 10 i i NOUN ejpam-2219 135 11 ) ) PUNCT ejpam-2219 135 12 the the DET ejpam-2219 135 13 classical classical ADJ ejpam-2219 135 14 solutions solution NOUN ejpam-2219 135 15 to to ADP ejpam-2219 135 16 nonlinear nonlinear ADJ ejpam-2219 135 17 field field NOUN ejpam-2219 135 18 equations equation NOUN ejpam-2219 135 19 give give VERB ejpam-2219 135 20 us we PRON ejpam-2219 135 21 insight insight NOUN ejpam-2219 135 22 into into ADP ejpam-2219 135 23 the the DET ejpam-2219 135 24 bound bound ADJ ejpam-2219 135 25 state state NOUN ejpam-2219 135 26 behavior behavior NOUN ejpam-2219 135 27 of of ADP ejpam-2219 135 28 field field NOUN ejpam-2219 135 29 theories theory NOUN ejpam-2219 135 30 , , PUNCT ejpam-2219 135 31 particular particular ADJ ejpam-2219 135 32 interest interest NOUN ejpam-2219 135 33 are be AUX ejpam-2219 135 34 new new ADJ ejpam-2219 135 35 class class NOUN ejpam-2219 135 36 of of ADP ejpam-2219 135 37 classical classical ADJ ejpam-2219 135 38 solutions solution NOUN ejpam-2219 135 39 of of ADP ejpam-2219 135 40 the the DET ejpam-2219 135 41 yang yang PROPN ejpam-2219 135 42 mills mills PROPN ejpam-2219 135 43 equations equation NOUN ejpam-2219 135 44 . . PUNCT ejpam-2219 136 1 ( ( PUNCT ejpam-2219 136 2 ii ii X ejpam-2219 136 3 ) ) PUNCT ejpam-2219 136 4 we we PRON ejpam-2219 136 5 chose choose VERB ejpam-2219 136 6 the the DET ejpam-2219 136 7 group group NOUN ejpam-2219 136 8 su(2 su(2 NOUN ejpam-2219 136 9 ) ) PUNCT ejpam-2219 136 10 because because SCONJ ejpam-2219 136 11 we we PRON ejpam-2219 136 12 wanted want VERB ejpam-2219 136 13 to to PART ejpam-2219 136 14 include include VERB ejpam-2219 136 15 explicit explicit ADJ ejpam-2219 136 16 time time NOUN ejpam-2219 136 17 - - PUNCT ejpam-2219 136 18 dependence dependence NOUN ejpam-2219 136 19 in in ADP ejpam-2219 136 20 the the DET ejpam-2219 136 21 classical classical ADJ ejpam-2219 136 22 soltions soltion NOUN ejpam-2219 136 23 of of ADP ejpam-2219 136 24 the the DET ejpam-2219 136 25 yang yang PROPN ejpam-2219 136 26 mills mills PROPN ejpam-2219 136 27 equations equation NOUN ejpam-2219 136 28 , , PUNCT ejpam-2219 136 29 this this PRON ejpam-2219 136 30 does do AUX ejpam-2219 136 31 not not PART ejpam-2219 136 32 exclude exclude VERB ejpam-2219 136 33 eventually eventually ADV ejpam-2219 136 34 using use VERB ejpam-2219 136 35 higher high ADJ ejpam-2219 136 36 groups group NOUN ejpam-2219 136 37 . . PUNCT ejpam-2219 137 1 ( ( PUNCT ejpam-2219 137 2 iii iii X ejpam-2219 137 3 ) ) PUNCT ejpam-2219 137 4 we we PRON ejpam-2219 137 5 solved solve VERB ejpam-2219 137 6 the the DET ejpam-2219 137 7 nonlinear nonlinear PROPN ejpam-2219 137 8 yang yang PROPN ejpam-2219 137 9 -mills -mills PROPN ejpam-2219 137 10 equation equation NOUN ejpam-2219 137 11 by by ADP ejpam-2219 137 12 using use VERB ejpam-2219 137 13 the the DET ejpam-2219 137 14 time time NOUN ejpam-2219 137 15 -dependent -dependent ADJ ejpam-2219 137 16 solutions solution NOUN ejpam-2219 137 17 of of ADP ejpam-2219 137 18 electrodynamics electrodynamic NOUN ejpam-2219 137 19 , , PUNCT ejpam-2219 137 20 the the DET ejpam-2219 137 21 physical physical ADJ ejpam-2219 137 22 picture picture NOUN ejpam-2219 137 23 is be AUX ejpam-2219 137 24 as as SCONJ ejpam-2219 137 25 follows follow VERB ejpam-2219 137 26 : : PUNCT ejpam-2219 137 27 due due ADP ejpam-2219 137 28 to to ADP ejpam-2219 137 29 the the DET ejpam-2219 137 30 influence influence NOUN ejpam-2219 137 31 of of ADP ejpam-2219 137 32 an an DET ejpam-2219 137 33 external external ADJ ejpam-2219 137 34 field field NOUN ejpam-2219 137 35 , , PUNCT ejpam-2219 137 36 this this DET ejpam-2219 137 37 particle particle NOUN ejpam-2219 137 38 , , PUNCT ejpam-2219 137 39 because because SCONJ ejpam-2219 137 40 it it PRON ejpam-2219 137 41 is be AUX ejpam-2219 137 42 accelerating accelerate VERB ejpam-2219 137 43 , , PUNCT ejpam-2219 137 44 produces produce VERB ejpam-2219 137 45 a a DET ejpam-2219 137 46 gauge gauge ADJ ejpam-2219 137 47 potential potential NOUN ejpam-2219 137 48 aµ aµ NOUN ejpam-2219 137 49 obeying obey VERB ejpam-2219 137 50 ( ( PUNCT ejpam-2219 137 51 50 50 NUM ejpam-2219 137 52 ) ) PUNCT ejpam-2219 137 53 . . PUNCT ejpam-2219 138 1 this this DET ejpam-2219 138 2 gauge gauge ADJ ejpam-2219 138 3 potential potential NOUN ejpam-2219 138 4 , , PUNCT ejpam-2219 138 5 in in ADP ejpam-2219 138 6 turn turn NOUN ejpam-2219 138 7 , , PUNCT ejpam-2219 138 8 can can AUX ejpam-2219 138 9 be be AUX ejpam-2219 138 10 used use VERB ejpam-2219 138 11 to to PART ejpam-2219 138 12 form form VERB ejpam-2219 138 13 the the DET ejpam-2219 138 14 ansatz ansatz ADJ ejpam-2219 138 15 ( ( PUNCT ejpam-2219 138 16 50 50 NUM ejpam-2219 138 17 ) ) PUNCT ejpam-2219 138 18 , , PUNCT ejpam-2219 138 19 which which PRON ejpam-2219 138 20 exactly exactly ADV ejpam-2219 138 21 solves solve VERB ejpam-2219 138 22 the the DET ejpam-2219 138 23 nonlinear nonlinear PROPN ejpam-2219 138 24 yang yang PROPN ejpam-2219 138 25 - - PUNCT ejpam-2219 138 26 mills mill NOUN ejpam-2219 138 27 equation equation NOUN ejpam-2219 138 28 . . PUNCT ejpam-2219 139 1 4 4 X ejpam-2219 139 2 . . X ejpam-2219 139 3 conclusions conclusion NOUN ejpam-2219 139 4 a a DET ejpam-2219 139 5 soliton soliton NOUN ejpam-2219 139 6 is be AUX ejpam-2219 139 7 a a DET ejpam-2219 139 8 localized localized ADJ ejpam-2219 139 9 pulse pulse NOUN ejpam-2219 139 10 - - PUNCT ejpam-2219 139 11 like like ADJ ejpam-2219 139 12 nonlinear nonlinear ADJ ejpam-2219 139 13 wave wave NOUN ejpam-2219 139 14 that that PRON ejpam-2219 139 15 possesses possess VERB ejpam-2219 139 16 remarkable remarkable ADJ ejpam-2219 139 17 stability stability NOUN ejpam-2219 139 18 properties property NOUN ejpam-2219 139 19 . . PUNCT ejpam-2219 140 1 typically typically ADV ejpam-2219 140 2 , , PUNCT ejpam-2219 140 3 problems problem NOUN ejpam-2219 140 4 that that PRON ejpam-2219 140 5 admit admit VERB ejpam-2219 140 6 soliton soliton NOUN ejpam-2219 140 7 solutions solution NOUN ejpam-2219 140 8 are be AUX ejpam-2219 140 9 in in ADP ejpam-2219 140 10 the the DET ejpam-2219 140 11 form form NOUN ejpam-2219 140 12 of of ADP ejpam-2219 140 13 evolution evolution NOUN ejpam-2219 140 14 equations equation NOUN ejpam-2219 140 15 that that PRON ejpam-2219 140 16 describe describe VERB ejpam-2219 140 17 how how SCONJ ejpam-2219 140 18 some some DET ejpam-2219 140 19 variable variable NOUN ejpam-2219 140 20 or or CCONJ ejpam-2219 140 21 set set NOUN ejpam-2219 140 22 of of ADP ejpam-2219 140 23 variables variable NOUN ejpam-2219 140 24 evolve evolve VERB ejpam-2219 140 25 in in ADP ejpam-2219 140 26 time time NOUN ejpam-2219 140 27 from from ADP ejpam-2219 140 28 a a DET ejpam-2219 140 29 given give VERB ejpam-2219 140 30 state state NOUN ejpam-2219 140 31 . . PUNCT ejpam-2219 141 1 the the DET ejpam-2219 141 2 equations equation NOUN ejpam-2219 141 3 may may AUX ejpam-2219 141 4 take take VERB ejpam-2219 141 5 a a DET ejpam-2219 141 6 variety variety NOUN ejpam-2219 141 7 of of ADP ejpam-2219 141 8 forms form NOUN ejpam-2219 141 9 , , PUNCT ejpam-2219 141 10 for for ADP ejpam-2219 141 11 example example NOUN ejpam-2219 141 12 , , PUNCT ejpam-2219 141 13 pdes pde NOUN ejpam-2219 141 14 , , PUNCT ejpam-2219 141 15 differential differential ADJ ejpam-2219 141 16 difference difference NOUN ejpam-2219 141 17 equations equation NOUN ejpam-2219 141 18 , , PUNCT ejpam-2219 141 19 partial partial ADJ ejpam-2219 141 20 difference difference NOUN ejpam-2219 141 21 equations equation NOUN ejpam-2219 141 22 , , PUNCT ejpam-2219 141 23 and and CCONJ ejpam-2219 141 24 integro integro ADJ ejpam-2219 141 25 - - PUNCT ejpam-2219 141 26 differential differential NOUN ejpam-2219 141 27 equations equation NOUN ejpam-2219 141 28 , , PUNCT ejpam-2219 141 29 as as ADV ejpam-2219 141 30 well well ADV ejpam-2219 141 31 as as ADP ejpam-2219 141 32 coupled couple VERB ejpam-2219 141 33 odes ode NOUN ejpam-2219 141 34 of of ADP ejpam-2219 141 35 finite finite ADJ ejpam-2219 141 36 order order NOUN ejpam-2219 141 37 . . PUNCT ejpam-2219 142 1 in in ADP ejpam-2219 142 2 this this DET ejpam-2219 142 3 paper paper NOUN ejpam-2219 142 4 , , PUNCT ejpam-2219 142 5 we we PRON ejpam-2219 142 6 considered consider VERB ejpam-2219 142 7 the the DET ejpam-2219 142 8 construction construction NOUN ejpam-2219 142 9 of of ADP ejpam-2219 142 10 exact exact ADJ ejpam-2219 142 11 solutions solution NOUN ejpam-2219 142 12 to to ADP ejpam-2219 142 13 cgl cgl NOUN ejpam-2219 142 14 equation equation NOUN ejpam-2219 142 15 . . PUNCT ejpam-2219 143 1 we we PRON ejpam-2219 143 2 obtain obtain VERB ejpam-2219 143 3 traveling travel VERB ejpam-2219 143 4 wave wave NOUN ejpam-2219 143 5 solutions solution NOUN ejpam-2219 143 6 for for ADP ejpam-2219 143 7 the the DET ejpam-2219 143 8 above above ADJ ejpam-2219 143 9 equations equation NOUN ejpam-2219 143 10 by by ADP ejpam-2219 143 11 using use VERB ejpam-2219 143 12 bts bt NOUN ejpam-2219 143 13 method method NOUN ejpam-2219 143 14 with with ADP ejpam-2219 143 15 the the DET ejpam-2219 143 16 aid aid NOUN ejpam-2219 143 17 of of ADP ejpam-2219 143 18 mathematica mathematica PROPN ejpam-2219 143 19 . . PUNCT ejpam-2219 144 1 the the DET ejpam-2219 144 2 soliton soliton NOUN ejpam-2219 144 3 phenomena phenomenon NOUN ejpam-2219 144 4 and and CCONJ ejpam-2219 144 5 integrable integrable ADJ ejpam-2219 144 6 nlees nlee NOUN ejpam-2219 144 7 represent represent VERB ejpam-2219 144 8 an an DET ejpam-2219 144 9 important important ADJ ejpam-2219 144 10 and and CCONJ ejpam-2219 144 11 well well ADV ejpam-2219 144 12 established establish VERB ejpam-2219 144 13 field field NOUN ejpam-2219 144 14 of of ADP ejpam-2219 144 15 modern modern ADJ ejpam-2219 144 16 physics physic NOUN ejpam-2219 144 17 , , PUNCT ejpam-2219 144 18 mathematical mathematical ADJ ejpam-2219 144 19 physics physics NOUN ejpam-2219 144 20 and and CCONJ ejpam-2219 144 21 applied apply VERB ejpam-2219 144 22 mathematics mathematic NOUN ejpam-2219 144 23 . . PUNCT ejpam-2219 145 1 solitons soliton NOUN ejpam-2219 145 2 are be AUX ejpam-2219 145 3 found find VERB ejpam-2219 145 4 in in ADP ejpam-2219 145 5 various various ADJ ejpam-2219 145 6 areas area NOUN ejpam-2219 145 7 of of ADP ejpam-2219 145 8 physics physics NOUN ejpam-2219 145 9 from from ADP ejpam-2219 145 10 hydrodynamics hydrodynamic NOUN ejpam-2219 145 11 and and CCONJ ejpam-2219 145 12 plasma plasma NOUN ejpam-2219 145 13 physics physic NOUN ejpam-2219 145 14 , , PUNCT ejpam-2219 145 15 nonlinear nonlinear ADJ ejpam-2219 145 16 optics optic NOUN ejpam-2219 145 17 and and CCONJ ejpam-2219 145 18 solid solid ADJ ejpam-2219 145 19 state state NOUN ejpam-2219 145 20 physics physics NOUN ejpam-2219 145 21 , , PUNCT ejpam-2219 145 22 to to ADP ejpam-2219 145 23 field field NOUN ejpam-2219 145 24 theory theory NOUN ejpam-2219 145 25 and and CCONJ ejpam-2219 145 26 gravitation gravitation NOUN ejpam-2219 145 27 . . PUNCT ejpam-2219 146 1 nlees nlee NOUN ejpam-2219 146 2 which which PRON ejpam-2219 146 3 describe describe VERB ejpam-2219 146 4 soli soli ADJ ejpam-2219 146 5 - - PUNCT ejpam-2219 146 6 ton ton NOUN ejpam-2219 146 7 phenomena phenomenon NOUN ejpam-2219 146 8 have have VERB ejpam-2219 146 9 an an DET ejpam-2219 146 10 universal universal ADJ ejpam-2219 146 11 character character NOUN ejpam-2219 146 12 . . PUNCT ejpam-2219 147 1 references reference NOUN ejpam-2219 147 2 571 571 NUM ejpam-2219 147 3 a a DET ejpam-2219 147 4 traveling travel VERB ejpam-2219 147 5 wave wave NOUN ejpam-2219 147 6 of of ADP ejpam-2219 147 7 permanent permanent ADJ ejpam-2219 147 8 form form NOUN ejpam-2219 147 9 has have AUX ejpam-2219 147 10 already already ADV ejpam-2219 147 11 been be AUX ejpam-2219 147 12 met meet VERB ejpam-2219 147 13 ; ; PUNCT ejpam-2219 147 14 this this PRON ejpam-2219 147 15 is be AUX ejpam-2219 147 16 the the DET ejpam-2219 147 17 solitary solitary ADJ ejpam-2219 147 18 wave wave NOUN ejpam-2219 147 19 solution solution NOUN ejpam-2219 147 20 of of ADP ejpam-2219 147 21 the the DET ejpam-2219 147 22 nlee nlee NOUN ejpam-2219 147 23 itself itself PRON ejpam-2219 147 24 . . PUNCT ejpam-2219 148 1 such such DET ejpam-2219 148 2 a a DET ejpam-2219 148 3 wave wave NOUN ejpam-2219 148 4 is be AUX ejpam-2219 148 5 a a DET ejpam-2219 148 6 special special ADJ ejpam-2219 148 7 solution solution NOUN ejpam-2219 148 8 of of ADP ejpam-2219 148 9 the the DET ejpam-2219 148 10 governing govern VERB ejpam-2219 148 11 equation equation NOUN ejpam-2219 148 12 which which PRON ejpam-2219 148 13 does do AUX ejpam-2219 148 14 not not PART ejpam-2219 148 15 change change VERB ejpam-2219 148 16 its its PRON ejpam-2219 148 17 shape shape NOUN ejpam-2219 148 18 and and CCONJ ejpam-2219 148 19 which which PRON ejpam-2219 148 20 propagates propagate VERB ejpam-2219 148 21 at at ADP ejpam-2219 148 22 constant constant ADJ ejpam-2219 148 23 speed speed NOUN ejpam-2219 148 24 . . PUNCT ejpam-2219 149 1 the the DET ejpam-2219 149 2 sdym sdym ADJ ejpam-2219 149 3 equations equation NOUN ejpam-2219 149 4 play play VERB ejpam-2219 149 5 a a DET ejpam-2219 149 6 central central ADJ ejpam-2219 149 7 role role NOUN ejpam-2219 149 8 in in ADP ejpam-2219 149 9 the the DET ejpam-2219 149 10 field field NOUN ejpam-2219 149 11 of of ADP ejpam-2219 149 12 integrable integrable ADJ ejpam-2219 149 13 systems system NOUN ejpam-2219 149 14 and and CCONJ ejpam-2219 149 15 also also ADV ejpam-2219 149 16 play play VERB ejpam-2219 149 17 a a DET ejpam-2219 149 18 fundamental fundamental ADJ ejpam-2219 149 19 role role NOUN ejpam-2219 149 20 in in ADP ejpam-2219 149 21 several several ADJ ejpam-2219 149 22 other other ADJ ejpam-2219 149 23 areas area NOUN ejpam-2219 149 24 of of ADP ejpam-2219 149 25 mathematics mathematic NOUN ejpam-2219 149 26 and and CCONJ ejpam-2219 149 27 physics physics NOUN ejpam-2219 149 28 . . PUNCT ejpam-2219 150 1 in in ADP ejpam-2219 150 2 addition addition NOUN ejpam-2219 150 3 the the DET ejpam-2219 150 4 sdym sdym ADJ ejpam-2219 150 5 equations equation NOUN ejpam-2219 150 6 are be AUX ejpam-2219 150 7 a a DET ejpam-2219 150 8 rich rich ADJ ejpam-2219 150 9 source source NOUN ejpam-2219 150 10 of of ADP ejpam-2219 150 11 integrable integrable ADJ ejpam-2219 150 12 systems system NOUN ejpam-2219 150 13 suggested suggest VERB ejpam-2219 150 14 by by ADP ejpam-2219 150 15 the the DET ejpam-2219 150 16 fact fact NOUN ejpam-2219 150 17 that that SCONJ ejpam-2219 150 18 they they PRON ejpam-2219 150 19 are be AUX ejpam-2219 150 20 the the DET ejpam-2219 150 21 compatibility compatibility NOUN ejpam-2219 150 22 condition condition NOUN ejpam-2219 150 23 of of ADP ejpam-2219 150 24 an an DET ejpam-2219 150 25 associated associated ADJ ejpam-2219 150 26 linear linear NOUN ejpam-2219 150 27 problem problem NOUN ejpam-2219 150 28 which which PRON ejpam-2219 150 29 admits admit VERB ejpam-2219 150 30 enormous enormous ADJ ejpam-2219 150 31 freedom freedom NOUN ejpam-2219 150 32 if if SCONJ ejpam-2219 150 33 one one PRON ejpam-2219 150 34 allows allow VERB ejpam-2219 150 35 the the DET ejpam-2219 150 36 associated associated ADJ ejpam-2219 150 37 gauge gauge NOUN ejpam-2219 150 38 algebra algebra NOUN ejpam-2219 150 39 to to PART ejpam-2219 150 40 be be AUX ejpam-2219 150 41 arbitrary arbitrary ADJ ejpam-2219 150 42 . . PUNCT ejpam-2219 151 1 the the DET ejpam-2219 151 2 classical classical ADJ ejpam-2219 151 3 soliton soliton NOUN ejpam-2219 151 4 equations equation NOUN ejpam-2219 151 5 in in ADP ejpam-2219 151 6 1 1 NUM ejpam-2219 151 7 + + PROPN ejpam-2219 151 8 1 1 NUM ejpam-2219 151 9 , , PUNCT ejpam-2219 151 10 2 2 NUM ejpam-2219 151 11 + + SYM ejpam-2219 151 12 1 1 NUM ejpam-2219 151 13 and and CCONJ ejpam-2219 151 14 3 3 NUM ejpam-2219 151 15 + + SYM ejpam-2219 151 16 1 1 NUM ejpam-2219 151 17 dimensions dimension NOUN ejpam-2219 151 18 are be AUX ejpam-2219 151 19 reductions reduction NOUN ejpam-2219 151 20 of of ADP ejpam-2219 151 21 the the DET ejpam-2219 151 22 sdym sdym ADJ ejpam-2219 151 23 equations equation NOUN ejpam-2219 151 24 with with ADP ejpam-2219 151 25 finite finite ADJ ejpam-2219 151 26 - - ADJ ejpam-2219 151 27 dimensional dimensional ADJ ejpam-2219 151 28 gauge gauge NOUN ejpam-2219 151 29 algebra algebra NOUN ejpam-2219 151 30 . . PUNCT ejpam-2219 152 1 in in ADP ejpam-2219 152 2 this this DET ejpam-2219 152 3 paper paper NOUN ejpam-2219 152 4 we we PRON ejpam-2219 152 5 have have AUX ejpam-2219 152 6 demonstrated demonstrate VERB ejpam-2219 152 7 the the DET ejpam-2219 152 8 reductions reduction NOUN ejpam-2219 152 9 of of ADP ejpam-2219 152 10 the the DET ejpam-2219 152 11 sdym sdym ADJ ejpam-2219 152 12 equations equation NOUN ejpam-2219 152 13 to to ADP ejpam-2219 152 14 cgl cgl NOUN ejpam-2219 152 15 equation equation NOUN ejpam-2219 152 16 and and CCONJ ejpam-2219 152 17 also also ADV ejpam-2219 152 18 obtained obtain VERB ejpam-2219 152 19 traveling travel VERB ejpam-2219 152 20 wave wave NOUN ejpam-2219 152 21 solution solution NOUN ejpam-2219 152 22 . . PUNCT ejpam-2219 153 1 references reference NOUN ejpam-2219 153 2 [ [ X ejpam-2219 153 3 1 1 NUM ejpam-2219 153 4 ] ] PUNCT ejpam-2219 153 5 m m VERB ejpam-2219 153 6 ablowitz ablowitz NOUN ejpam-2219 153 7 , , PUNCT ejpam-2219 153 8 s s PART ejpam-2219 153 9 chakravarty chakravarty NOUN ejpam-2219 153 10 , , PUNCT ejpam-2219 153 11 and and CCONJ ejpam-2219 153 12 r r NOUN ejpam-2219 153 13 halburd halburd NOUN ejpam-2219 153 14 . . PUNCT ejpam-2219 154 1 the the DET ejpam-2219 154 2 generalized generalize VERB ejpam-2219 154 3 chazy chazy ADJ ejpam-2219 154 4 equation equation NOUN ejpam-2219 154 5 and and CCONJ ejpam-2219 154 6 schwarzian schwarzian NOUN ejpam-2219 154 7 triangle triangle NOUN ejpam-2219 154 8 functions function NOUN ejpam-2219 154 9 . . PUNCT ejpam-2219 155 1 asian asian ADJ ejpam-2219 155 2 journal journal PROPN ejpam-2219 155 3 of of ADP ejpam-2219 155 4 mathematics mathematic NOUN ejpam-2219 155 5 , , PUNCT ejpam-2219 155 6 2:619–624 2:619–624 NOUN ejpam-2219 155 7 , , PUNCT ejpam-2219 155 8 1998 1998 NUM ejpam-2219 155 9 . . PUNCT ejpam-2219 156 1 [ [ X ejpam-2219 156 2 2 2 NUM ejpam-2219 156 3 ] ] PUNCT ejpam-2219 156 4 m m VERB ejpam-2219 156 5 ablowitz ablowitz NOUN ejpam-2219 156 6 , , PUNCT ejpam-2219 156 7 s s PART ejpam-2219 156 8 chakravarty chakravarty NOUN ejpam-2219 156 9 , , PUNCT ejpam-2219 156 10 and and CCONJ ejpam-2219 156 11 r r NOUN ejpam-2219 156 12 halburd halburd NOUN ejpam-2219 156 13 . . PUNCT ejpam-2219 157 1 on on ADP ejpam-2219 157 2 painlevé painlevé NOUN ejpam-2219 157 3 and and CCONJ ejpam-2219 157 4 darboux darboux VERB ejpam-2219 157 5 - - PUNCT ejpam-2219 157 6 halphen halphen ADV ejpam-2219 157 7 type type NOUN ejpam-2219 157 8 equations equation NOUN ejpam-2219 157 9 , , PUNCT ejpam-2219 157 10 in in ADP ejpam-2219 157 11 the the DET ejpam-2219 157 12 painlevé painlevé NOUN ejpam-2219 157 13 property property NOUN ejpam-2219 157 14 , , PUNCT ejpam-2219 157 15 one one NUM ejpam-2219 157 16 century century NOUN ejpam-2219 157 17 later later ADV ejpam-2219 157 18 , , PUNCT ejpam-2219 157 19 edited edit VERB ejpam-2219 157 20 by by ADP ejpam-2219 157 21 r. r. PROPN ejpam-2219 157 22 conte conte PROPN ejpam-2219 157 23 , , PUNCT ejpam-2219 157 24 crm crm PROPN ejpam-2219 157 25 series series PROPN ejpam-2219 157 26 in in ADP ejpam-2219 157 27 mathematical mathematical ADJ ejpam-2219 157 28 physics physics NOUN ejpam-2219 157 29 . . PUNCT ejpam-2219 157 30 , , PUNCT ejpam-2219 157 31 1998 1998 NUM ejpam-2219 157 32 . . PUNCT ejpam-2219 158 1 [ [ X ejpam-2219 158 2 3 3 NUM ejpam-2219 158 3 ] ] PUNCT ejpam-2219 158 4 m m VERB ejpam-2219 158 5 ablowitz ablowitz NOUN ejpam-2219 158 6 , , PUNCT ejpam-2219 158 7 s s PART ejpam-2219 158 8 chakravarty chakravarty NOUN ejpam-2219 158 9 , , PUNCT ejpam-2219 158 10 and and CCONJ ejpam-2219 158 11 r r NOUN ejpam-2219 158 12 halburd halburd NOUN ejpam-2219 158 13 . . PUNCT ejpam-2219 159 1 the the DET ejpam-2219 159 2 generalized generalize VERB ejpam-2219 159 3 chazy chazy ADJ ejpam-2219 159 4 equation equation NOUN ejpam-2219 159 5 from from ADP ejpam-2219 159 6 the the DET ejpam-2219 159 7 self self NOUN ejpam-2219 159 8 - - PUNCT ejpam-2219 159 9 duality duality NOUN ejpam-2219 159 10 equations equation NOUN ejpam-2219 159 11 . . PUNCT ejpam-2219 160 1 studies study NOUN ejpam-2219 160 2 in in ADP ejpam-2219 160 3 applied applied ADJ ejpam-2219 160 4 mathematics mathematic NOUN ejpam-2219 160 5 , , PUNCT ejpam-2219 160 6 103(1):75–88 103(1):75–88 NUM ejpam-2219 160 7 , , PUNCT ejpam-2219 160 8 1999 1999 NUM ejpam-2219 160 9 . . PUNCT ejpam-2219 161 1 [ [ X ejpam-2219 161 2 4 4 NUM ejpam-2219 161 3 ] ] PUNCT ejpam-2219 161 4 m m VERB ejpam-2219 161 5 ablowitz ablowitz NOUN ejpam-2219 161 6 , , PUNCT ejpam-2219 161 7 s s PART ejpam-2219 161 8 chakravarty chakravarty NOUN ejpam-2219 161 9 , , PUNCT ejpam-2219 161 10 and and CCONJ ejpam-2219 161 11 r r NOUN ejpam-2219 161 12 halburd halburd NOUN ejpam-2219 161 13 . . PUNCT ejpam-2219 162 1 integrable integrable ADJ ejpam-2219 162 2 systems system NOUN ejpam-2219 162 3 and and CCONJ ejpam-2219 162 4 reductions reduction NOUN ejpam-2219 162 5 of of ADP ejpam-2219 162 6 the the DET ejpam-2219 162 7 self self NOUN ejpam-2219 162 8 - - PUNCT ejpam-2219 162 9 dual dual ADJ ejpam-2219 162 10 yang yang PROPN ejpam-2219 162 11 – – PUNCT ejpam-2219 162 12 mills mill NOUN ejpam-2219 162 13 equations equation NOUN ejpam-2219 162 14 . . PUNCT ejpam-2219 163 1 journal journal PROPN ejpam-2219 163 2 of of ADP ejpam-2219 163 3 mathematical mathematical ADJ ejpam-2219 163 4 physics physics NOUN ejpam-2219 163 5 , , PUNCT ejpam-2219 163 6 44(8):3147–3173 44(8):3147–3173 PROPN ejpam-2219 163 7 , , PUNCT ejpam-2219 163 8 2003 2003 NUM ejpam-2219 163 9 . . PUNCT ejpam-2219 164 1 [ [ X ejpam-2219 164 2 5 5 NUM ejpam-2219 164 3 ] ] PUNCT ejpam-2219 164 4 m m VERB ejpam-2219 164 5 ablowitz ablowitz NOUN ejpam-2219 164 6 , , PUNCT ejpam-2219 164 7 s s PART ejpam-2219 164 8 chakravarty chakravarty NOUN ejpam-2219 164 9 , , PUNCT ejpam-2219 164 10 and and CCONJ ejpam-2219 164 11 l l PROPN ejpam-2219 164 12 takhtajan takhtajan PROPN ejpam-2219 164 13 . . PUNCT ejpam-2219 165 1 a a DET ejpam-2219 165 2 self self NOUN ejpam-2219 165 3 - - PUNCT ejpam-2219 165 4 dual dual ADJ ejpam-2219 165 5 yang yang PROPN ejpam-2219 165 6 - - PUNCT ejpam-2219 165 7 mills mill NOUN ejpam-2219 165 8 hierarchy hierarchy NOUN ejpam-2219 165 9 and and CCONJ ejpam-2219 165 10 its its PRON ejpam-2219 165 11 reductions reduction NOUN ejpam-2219 165 12 to to PART ejpam-2219 165 13 integrable integrable VERB ejpam-2219 165 14 systems system NOUN ejpam-2219 165 15 in in ADP ejpam-2219 165 16 1 1 NUM ejpam-2219 165 17 + + SYM ejpam-2219 165 18 1 1 NUM ejpam-2219 165 19 and and CCONJ ejpam-2219 165 20 2 2 NUM ejpam-2219 165 21 + + SYM ejpam-2219 165 22 1 1 NUM ejpam-2219 165 23 dimensions dimension NOUN ejpam-2219 165 24 . . PUNCT ejpam-2219 166 1 communications communication NOUN ejpam-2219 166 2 in in ADP ejpam-2219 166 3 mathematical mathematical ADJ ejpam-2219 166 4 physics physics NOUN ejpam-2219 166 5 , , PUNCT ejpam-2219 166 6 158(2):289–314 158(2):289–314 NUM ejpam-2219 166 7 , , PUNCT ejpam-2219 166 8 1993 1993 NUM ejpam-2219 166 9 . . PUNCT ejpam-2219 167 1 [ [ X ejpam-2219 167 2 6 6 NUM ejpam-2219 167 3 ] ] PUNCT ejpam-2219 167 4 m m VERB ejpam-2219 167 5 ablowitz ablowitz NOUN ejpam-2219 167 6 and and CCONJ ejpam-2219 167 7 p p PROPN ejpam-2219 167 8 clarkson clarkson PROPN ejpam-2219 167 9 . . PUNCT ejpam-2219 168 1 solitons soliton NOUN ejpam-2219 168 2 , , PUNCT ejpam-2219 168 3 nonlinear nonlinear ADJ ejpam-2219 168 4 evolution evolution NOUN ejpam-2219 168 5 equations equation NOUN ejpam-2219 168 6 and and CCONJ ejpam-2219 168 7 inverse inverse NOUN ejpam-2219 168 8 scattering scattering NOUN ejpam-2219 168 9 , , PUNCT ejpam-2219 168 10 volume volume NOUN ejpam-2219 168 11 149 149 NUM ejpam-2219 168 12 . . PUNCT ejpam-2219 169 1 cambridge cambridge PROPN ejpam-2219 169 2 university university PROPN ejpam-2219 169 3 press press NOUN ejpam-2219 169 4 , , PUNCT ejpam-2219 169 5 1991 1991 NUM ejpam-2219 169 6 . . PUNCT ejpam-2219 170 1 [ [ X ejpam-2219 170 2 7 7 X ejpam-2219 170 3 ] ] PUNCT ejpam-2219 170 4 m m VERB ejpam-2219 170 5 ablowitz ablowitz NOUN ejpam-2219 170 6 , , PUNCT ejpam-2219 170 7 d d NOUN ejpam-2219 170 8 kaup kaup PROPN ejpam-2219 170 9 , , PUNCT ejpam-2219 170 10 and and CCONJ ejpam-2219 170 11 a a DET ejpam-2219 170 12 newell newell PROPN ejpam-2219 170 13 . . PUNCT ejpam-2219 171 1 the the DET ejpam-2219 171 2 inverse inverse NOUN ejpam-2219 171 3 scattering scattering NOUN ejpam-2219 171 4 transform transform VERB ejpam-2219 171 5 - - PUNCT ejpam-2219 171 6 fourier fourier NOUN ejpam-2219 171 7 analysis analysis NOUN ejpam-2219 171 8 for for ADP ejpam-2219 171 9 nonlinear nonlinear ADJ ejpam-2219 171 10 problems problem NOUN ejpam-2219 171 11 . . PUNCT ejpam-2219 172 1 studies study NOUN ejpam-2219 172 2 in in ADP ejpam-2219 172 3 applied applied ADJ ejpam-2219 172 4 mathematics mathematic NOUN ejpam-2219 172 5 , , PUNCT ejpam-2219 172 6 53(4):249–315 53(4):249–315 PROPN ejpam-2219 172 7 , , PUNCT ejpam-2219 172 8 1974 1974 NUM ejpam-2219 172 9 . . PUNCT ejpam-2219 173 1 [ [ X ejpam-2219 173 2 8 8 NUM ejpam-2219 173 3 ] ] PUNCT ejpam-2219 173 4 m m NOUN ejpam-2219 173 5 atiyah atiyah NOUN ejpam-2219 173 6 and and CCONJ ejpam-2219 173 7 r r NOUN ejpam-2219 173 8 ward ward NOUN ejpam-2219 173 9 . . PUNCT ejpam-2219 174 1 instantons instanton NOUN ejpam-2219 174 2 and and CCONJ ejpam-2219 174 3 algebraic algebraic ADJ ejpam-2219 174 4 geometry geometry NOUN ejpam-2219 174 5 . . PUNCT ejpam-2219 175 1 communications communication NOUN ejpam-2219 175 2 in in ADP ejpam-2219 175 3 mathematical mathematical ADJ ejpam-2219 175 4 physics physics NOUN ejpam-2219 175 5 , , PUNCT ejpam-2219 175 6 55(2):117–124 55(2):117–124 PROPN ejpam-2219 175 7 , , PUNCT ejpam-2219 175 8 1977 1977 NUM ejpam-2219 175 9 . . PUNCT ejpam-2219 176 1 [ [ X ejpam-2219 176 2 9 9 NUM ejpam-2219 176 3 ] ] X ejpam-2219 176 4 r r NOUN ejpam-2219 176 5 beals beal NOUN ejpam-2219 176 6 , , PUNCT ejpam-2219 176 7 m m VERB ejpam-2219 176 8 rabelo rabelo NOUN ejpam-2219 176 9 , , PUNCT ejpam-2219 176 10 and and CCONJ ejpam-2219 176 11 k k PROPN ejpam-2219 176 12 tenenblat tenenblat NOUN ejpam-2219 176 13 . . PUNCT ejpam-2219 177 1 bäcklund bäcklund NOUN ejpam-2219 177 2 transformations transformation NOUN ejpam-2219 177 3 and and CCONJ ejpam-2219 177 4 inverse inverse NOUN ejpam-2219 177 5 scattering scatter VERB ejpam-2219 177 6 solutions solution NOUN ejpam-2219 177 7 for for ADP ejpam-2219 177 8 some some DET ejpam-2219 177 9 pseudospherical pseudospherical ADJ ejpam-2219 177 10 surface surface NOUN ejpam-2219 177 11 equations equation NOUN ejpam-2219 177 12 . . PUNCT ejpam-2219 178 1 studies study NOUN ejpam-2219 178 2 in in ADP ejpam-2219 178 3 applied applied ADJ ejpam-2219 178 4 mathematics mathematic NOUN ejpam-2219 178 5 , , PUNCT ejpam-2219 178 6 81(2):125–151 81(2):125–151 PROPN ejpam-2219 178 7 , , PUNCT ejpam-2219 178 8 1989 1989 NUM ejpam-2219 178 9 . . PUNCT ejpam-2219 179 1 references reference NOUN ejpam-2219 179 2 572 572 NUM ejpam-2219 179 3 [ [ SYM ejpam-2219 179 4 10 10 NUM ejpam-2219 179 5 ] ] X ejpam-2219 179 6 j j PROPN ejpam-2219 179 7 cavalcante cavalcante NOUN ejpam-2219 179 8 and and CCONJ ejpam-2219 179 9 k k PROPN ejpam-2219 179 10 tenenblat tenenblat NOUN ejpam-2219 179 11 . . PUNCT ejpam-2219 180 1 conservation conservation NOUN ejpam-2219 180 2 laws law NOUN ejpam-2219 180 3 for for ADP ejpam-2219 180 4 nonlinear nonlinear ADJ ejpam-2219 180 5 evolution evolution NOUN ejpam-2219 180 6 equations equation NOUN ejpam-2219 180 7 . . PUNCT ejpam-2219 181 1 journal journal PROPN ejpam-2219 181 2 of of ADP ejpam-2219 181 3 mathematical mathematical ADJ ejpam-2219 181 4 physics physics NOUN ejpam-2219 181 5 , , PUNCT ejpam-2219 181 6 29(4):1044–1049 29(4):1044–1049 NUM ejpam-2219 181 7 , , PUNCT ejpam-2219 181 8 1988 1988 NUM ejpam-2219 181 9 . . PUNCT ejpam-2219 182 1 [ [ X ejpam-2219 182 2 11 11 NUM ejpam-2219 182 3 ] ] X ejpam-2219 182 4 k k PROPN ejpam-2219 182 5 chadan chadan PROPN ejpam-2219 182 6 and and CCONJ ejpam-2219 182 7 p p PROPN ejpam-2219 182 8 sabatier sabatier NOUN ejpam-2219 182 9 . . PUNCT ejpam-2219 183 1 inverse inverse NOUN ejpam-2219 183 2 problems problem NOUN ejpam-2219 183 3 in in ADP ejpam-2219 183 4 quantum quantum NOUN ejpam-2219 183 5 scattering scattering NOUN ejpam-2219 183 6 theory theory NOUN ejpam-2219 183 7 . . PUNCT ejpam-2219 184 1 springerverlag springerverlag PROPN ejpam-2219 184 2 , , PUNCT ejpam-2219 184 3 new new PROPN ejpam-2219 184 4 york york PROPN ejpam-2219 184 5 , , PUNCT ejpam-2219 184 6 ny ny PROPN ejpam-2219 184 7 , , PUNCT ejpam-2219 184 8 1977 1977 NUM ejpam-2219 184 9 . . PUNCT ejpam-2219 185 1 [ [ X ejpam-2219 185 2 12 12 NUM ejpam-2219 185 3 ] ] X ejpam-2219 185 4 s s X ejpam-2219 185 5 chern chern NOUN ejpam-2219 185 6 and and CCONJ ejpam-2219 185 7 k k PROPN ejpam-2219 185 8 tenenblat tenenblat NOUN ejpam-2219 185 9 . . PUNCT ejpam-2219 186 1 pseudospherical pseudospherical ADJ ejpam-2219 186 2 surfaces surface NOUN ejpam-2219 186 3 and and CCONJ ejpam-2219 186 4 evolution evolution NOUN ejpam-2219 186 5 equations equation NOUN ejpam-2219 186 6 . . PUNCT ejpam-2219 187 1 studies study NOUN ejpam-2219 187 2 in in ADP ejpam-2219 187 3 applied applied ADJ ejpam-2219 187 4 mathematics mathematic NOUN ejpam-2219 187 5 , , PUNCT ejpam-2219 187 6 74(1):55–83 74(1):55–83 NUM ejpam-2219 187 7 , , PUNCT ejpam-2219 187 8 1986 1986 NUM ejpam-2219 187 9 . . PUNCT ejpam-2219 188 1 [ [ X ejpam-2219 188 2 13 13 NUM ejpam-2219 188 3 ] ] PUNCT ejpam-2219 188 4 t t PROPN ejpam-2219 188 5 chuu chuu PROPN ejpam-2219 188 6 and and CCONJ ejpam-2219 188 7 k k PROPN ejpam-2219 188 8 uhlenbeck uhlenbeck PROPN ejpam-2219 188 9 . . PROPN ejpam-2219 189 1 introduction introduction NOUN ejpam-2219 189 2 to to ADP ejpam-2219 189 3 surveys survey NOUN ejpam-2219 189 4 in in ADP ejpam-2219 189 5 differential differential ADJ ejpam-2219 189 6 geometry geometry NOUN ejpam-2219 189 7 : : PUNCT ejpam-2219 189 8 integrable integrable ADJ ejpam-2219 189 9 systems system NOUN ejpam-2219 189 10 , , PUNCT ejpam-2219 189 11 . . PUNCT ejpam-2219 190 1 surveys survey NOUN ejpam-2219 190 2 in in ADP ejpam-2219 190 3 differential differential ADJ ejpam-2219 190 4 geometry geometry NOUN ejpam-2219 190 5 , , PUNCT ejpam-2219 190 6 iv iv NUM ejpam-2219 190 7 , , PUNCT ejpam-2219 190 8 international international ADJ ejpam-2219 190 9 press press NOUN ejpam-2219 190 10 , , PUNCT ejpam-2219 190 11 boston boston PROPN ejpam-2219 190 12 , , PUNCT ejpam-2219 190 13 mass mass PROPN ejpam-2219 190 14 , , PUNCT ejpam-2219 190 15 usa usa PROPN ejpam-2219 190 16 , , PUNCT ejpam-2219 190 17 1998 1998 NUM ejpam-2219 190 18 . . PUNCT ejpam-2219 191 1 [ [ X ejpam-2219 191 2 14 14 NUM ejpam-2219 191 3 ] ] X ejpam-2219 191 4 r r NOUN ejpam-2219 191 5 donagi donagi NOUN ejpam-2219 191 6 and and CCONJ ejpam-2219 191 7 e e NOUN ejpam-2219 191 8 witten witten PROPN ejpam-2219 191 9 . . PUNCT ejpam-2219 192 1 supersymmetric supersymmetric PROPN ejpam-2219 192 2 yang yang PROPN ejpam-2219 192 3 - - PUNCT ejpam-2219 192 4 mills mill NOUN ejpam-2219 192 5 theory theory NOUN ejpam-2219 192 6 and and CCONJ ejpam-2219 192 7 integrable integrable ADJ ejpam-2219 192 8 systems system NOUN ejpam-2219 192 9 . . PUNCT ejpam-2219 193 1 nuclear nuclear ADJ ejpam-2219 193 2 physics physics PROPN ejpam-2219 193 3 b b PROPN ejpam-2219 193 4 , , PUNCT ejpam-2219 193 5 460(2):299–334 460(2):299–334 PROPN ejpam-2219 193 6 , , PUNCT ejpam-2219 193 7 1996 1996 NUM ejpam-2219 193 8 . . PUNCT ejpam-2219 194 1 [ [ X ejpam-2219 194 2 15 15 NUM ejpam-2219 194 3 ] ] X ejpam-2219 194 4 r r NOUN ejpam-2219 194 5 hermann hermann PROPN ejpam-2219 194 6 . . PUNCT ejpam-2219 194 7 vector vector NOUN ejpam-2219 194 8 bundles bundle NOUN ejpam-2219 194 9 in in ADP ejpam-2219 194 10 mathematical mathematical ADJ ejpam-2219 194 11 physics physics NOUN ejpam-2219 194 12 , , PUNCT ejpam-2219 194 13 volume volume NOUN ejpam-2219 194 14 1 1 NUM ejpam-2219 194 15 . . PUNCT ejpam-2219 194 16 new new PROPN ejpam-2219 194 17 york york PROPN ejpam-2219 194 18 : : PUNCT ejpam-2219 194 19 benjamin benjamin PROPN ejpam-2219 194 20 , , PUNCT ejpam-2219 194 21 1970 1970 NUM ejpam-2219 194 22 . . PUNCT ejpam-2219 195 1 [ [ X ejpam-2219 195 2 16 16 NUM ejpam-2219 195 3 ] ] PUNCT ejpam-2219 195 4 n n PRON ejpam-2219 195 5 hitchin hitchin X ejpam-2219 195 6 . . PUNCT ejpam-2219 195 7 stable stable ADJ ejpam-2219 195 8 bundles bundle NOUN ejpam-2219 195 9 and and CCONJ ejpam-2219 195 10 integrable integrable ADJ ejpam-2219 195 11 systems system NOUN ejpam-2219 195 12 . . PUNCT ejpam-2219 196 1 duke duke PROPN ejpam-2219 196 2 mathematical mathematical PROPN ejpam-2219 196 3 journal journal PROPN ejpam-2219 196 4 , , PUNCT ejpam-2219 196 5 54(1):91–114 54(1):91–114 NUM ejpam-2219 196 6 , , PUNCT ejpam-2219 196 7 1987 1987 NUM ejpam-2219 196 8 . . PUNCT ejpam-2219 197 1 [ [ X ejpam-2219 197 2 17 17 NUM ejpam-2219 197 3 ] ] X ejpam-2219 197 4 j j PROPN ejpam-2219 197 5 bourguignon bourguignon PROPN ejpam-2219 197 6 , , PUNCT ejpam-2219 197 7 h h PROPN ejpam-2219 197 8 lawson lawson PROPN ejpam-2219 197 9 , , PUNCT ejpam-2219 197 10 and and CCONJ ejpam-2219 197 11 j j PROPN ejpam-2219 197 12 simons simons PROPN ejpam-2219 197 13 . . PUNCT ejpam-2219 198 1 stability stability NOUN ejpam-2219 198 2 and and CCONJ ejpam-2219 198 3 gap gap NOUN ejpam-2219 198 4 phenomena phenomenon NOUN ejpam-2219 198 5 for for ADP ejpam-2219 198 6 yang yang PROPN ejpam-2219 198 7 - - PUNCT ejpam-2219 198 8 mills mill NOUN ejpam-2219 198 9 fields field NOUN ejpam-2219 198 10 . . PUNCT ejpam-2219 199 1 proceedings proceeding NOUN ejpam-2219 199 2 of of ADP ejpam-2219 199 3 the the DET ejpam-2219 199 4 national national PROPN ejpam-2219 199 5 academy academy PROPN ejpam-2219 199 6 of of ADP ejpam-2219 199 7 sciences sciences PROPN ejpam-2219 199 8 , , PUNCT ejpam-2219 199 9 76(4):1550–1553 76(4):1550–1553 NOUN ejpam-2219 199 10 , , PUNCT ejpam-2219 199 11 1979 1979 NUM ejpam-2219 199 12 . . PUNCT ejpam-2219 200 1 [ [ X ejpam-2219 200 2 18 18 NUM ejpam-2219 200 3 ] ] PUNCT ejpam-2219 200 4 a a DET ejpam-2219 200 5 khater khater NOUN ejpam-2219 200 6 , , PUNCT ejpam-2219 200 7 a a DET ejpam-2219 200 8 abdalla abdalla PROPN ejpam-2219 200 9 , , PUNCT ejpam-2219 200 10 a a DET ejpam-2219 200 11 shehatah shehatah NOUN ejpam-2219 200 12 , , PUNCT ejpam-2219 200 13 d d PROPN ejpam-2219 200 14 callebaut callebaut PROPN ejpam-2219 200 15 , , PUNCT ejpam-2219 200 16 and and CCONJ ejpam-2219 200 17 s s AUX ejpam-2219 200 18 sayed say VERB ejpam-2219 200 19 . . PUNCT ejpam-2219 201 1 bäcklund bäcklund NOUN ejpam-2219 201 2 transformations transformation NOUN ejpam-2219 201 3 and and CCONJ ejpam-2219 201 4 exact exact ADJ ejpam-2219 201 5 solutions solution NOUN ejpam-2219 201 6 for for ADP ejpam-2219 201 7 self self NOUN ejpam-2219 201 8 - - PUNCT ejpam-2219 201 9 dual dual ADJ ejpam-2219 201 10 su(3 su(3 PROPN ejpam-2219 201 11 ) ) PUNCT ejpam-2219 201 12 yang yang PROPN ejpam-2219 201 13 - - PUNCT ejpam-2219 201 14 mills mill NOUN ejpam-2219 201 15 fields field NOUN ejpam-2219 201 16 . . PUNCT ejpam-2219 202 1 nuovo nuovo PROPN ejpam-2219 202 2 cimento cimento PROPN ejpam-2219 202 3 della della PROPN ejpam-2219 202 4 societa societa PROPN ejpam-2219 202 5 italiana italiana PROPN ejpam-2219 202 6 di di PROPN ejpam-2219 202 7 fisica fisica PROPN ejpam-2219 202 8 b b PROPN ejpam-2219 202 9 - - PUNCT ejpam-2219 202 10 general general ADJ ejpam-2219 202 11 eneral eneral ADJ ejpam-2219 202 12 physics physics NOUN ejpam-2219 202 13 relativity relativity NOUN ejpam-2219 202 14 astronomy astronomy NOUN ejpam-2219 202 15 and and CCONJ ejpam-2219 202 16 mathematical mathematical ADJ ejpam-2219 202 17 physics physics NOUN ejpam-2219 202 18 and and CCONJ ejpam-2219 202 19 methods method NOUN ejpam-2219 202 20 , , PUNCT ejpam-2219 202 21 114(1):1–9 114(1):1–9 NUM ejpam-2219 202 22 , , PUNCT ejpam-2219 202 23 1999 1999 NUM ejpam-2219 202 24 . . PUNCT ejpam-2219 203 1 [ [ X ejpam-2219 203 2 19 19 NUM ejpam-2219 203 3 ] ] PUNCT ejpam-2219 203 4 a a DET ejpam-2219 203 5 khater khater NOUN ejpam-2219 203 6 , , PUNCT ejpam-2219 203 7 d d PROPN ejpam-2219 203 8 callebaut callebaut PROPN ejpam-2219 203 9 , , PUNCT ejpam-2219 203 10 and and CCONJ ejpam-2219 203 11 s s AUX ejpam-2219 203 12 sayed say VERB ejpam-2219 203 13 . . PUNCT ejpam-2219 204 1 conservation conservation NOUN ejpam-2219 204 2 laws law NOUN ejpam-2219 204 3 for for ADP ejpam-2219 204 4 some some DET ejpam-2219 204 5 nonlinear nonlinear ADJ ejpam-2219 204 6 evolution evolution NOUN ejpam-2219 204 7 equations equation NOUN ejpam-2219 204 8 which which PRON ejpam-2219 204 9 describe describe VERB ejpam-2219 204 10 pseudo pseudo NOUN ejpam-2219 204 11 - - ADJ ejpam-2219 204 12 spherical spherical ADJ ejpam-2219 204 13 surfaces surface NOUN ejpam-2219 204 14 . . PUNCT ejpam-2219 205 1 journal journal NOUN ejpam-2219 205 2 of of ADP ejpam-2219 205 3 geometry geometry NOUN ejpam-2219 205 4 and and CCONJ ejpam-2219 205 5 physics physics NOUN ejpam-2219 205 6 , , PUNCT ejpam-2219 205 7 51(3):332–352 51(3):332–352 NOUN ejpam-2219 205 8 , , PUNCT ejpam-2219 205 9 2004 2004 NUM ejpam-2219 205 10 . . PUNCT ejpam-2219 206 1 [ [ X ejpam-2219 206 2 20 20 NUM ejpam-2219 206 3 ] ] PUNCT ejpam-2219 206 4 a a DET ejpam-2219 206 5 khater khater NOUN ejpam-2219 206 6 , , PUNCT ejpam-2219 206 7 d d PROPN ejpam-2219 206 8 callebaut callebaut PROPN ejpam-2219 206 9 , , PUNCT ejpam-2219 206 10 and and CCONJ ejpam-2219 206 11 s s AUX ejpam-2219 206 12 sayed say VERB ejpam-2219 206 13 . . PUNCT ejpam-2219 207 1 exact exact ADJ ejpam-2219 207 2 solutions solution NOUN ejpam-2219 207 3 for for ADP ejpam-2219 207 4 some some DET ejpam-2219 207 5 nonlinear nonlinear ADJ ejpam-2219 207 6 evolution evolution NOUN ejpam-2219 207 7 equations equation NOUN ejpam-2219 207 8 which which PRON ejpam-2219 207 9 describe describe VERB ejpam-2219 207 10 pseudo pseudo NOUN ejpam-2219 207 11 - - ADJ ejpam-2219 207 12 spherical spherical ADJ ejpam-2219 207 13 surfaces surface NOUN ejpam-2219 207 14 . . PUNCT ejpam-2219 208 1 journal journal NOUN ejpam-2219 208 2 of of ADP ejpam-2219 208 3 computational computational ADJ ejpam-2219 208 4 and and CCONJ ejpam-2219 208 5 applied applied ADJ ejpam-2219 208 6 mathematics mathematic NOUN ejpam-2219 208 7 , , PUNCT ejpam-2219 208 8 189(1):387–411 189(1):387–411 NUM ejpam-2219 208 9 , , PUNCT ejpam-2219 208 10 2006 2006 NUM ejpam-2219 208 11 . . PUNCT ejpam-2219 209 1 [ [ X ejpam-2219 209 2 21 21 NUM ejpam-2219 209 3 ] ] X ejpam-2219 209 4 a a DET ejpam-2219 209 5 khater khater NOUN ejpam-2219 209 6 , , PUNCT ejpam-2219 209 7 d d PROPN ejpam-2219 209 8 callebaut callebaut PROPN ejpam-2219 209 9 , , PUNCT ejpam-2219 209 10 a a DET ejpam-2219 209 11 shehata shehata NOUN ejpam-2219 209 12 , , PUNCT ejpam-2219 209 13 and and CCONJ ejpam-2219 209 14 s s AUX ejpam-2219 209 15 sayed say VERB ejpam-2219 209 16 . . PUNCT ejpam-2219 210 1 self self NOUN ejpam-2219 210 2 - - PUNCT ejpam-2219 210 3 dual dual ADJ ejpam-2219 210 4 solutions solution NOUN ejpam-2219 210 5 for for ADP ejpam-2219 210 6 su(2)and su(2)and PROPN ejpam-2219 210 7 su(3 su(3 PROPN ejpam-2219 210 8 ) ) PUNCT ejpam-2219 210 9 gauge gauge NOUN ejpam-2219 210 10 fields field NOUN ejpam-2219 210 11 on on ADP ejpam-2219 210 12 euclidean euclidean ADJ ejpam-2219 210 13 space space NOUN ejpam-2219 210 14 . . PUNCT ejpam-2219 211 1 international international ADJ ejpam-2219 211 2 journal journal PROPN ejpam-2219 211 3 of of ADP ejpam-2219 211 4 theoretical theoretical ADJ ejpam-2219 211 5 physics physics NOUN ejpam-2219 211 6 , , PUNCT ejpam-2219 211 7 43(1):151–159 43(1):151–159 PROPN ejpam-2219 211 8 , , PUNCT ejpam-2219 211 9 2004 2004 NUM ejpam-2219 211 10 . . PUNCT ejpam-2219 212 1 [ [ X ejpam-2219 212 2 22 22 NUM ejpam-2219 212 3 ] ] X ejpam-2219 212 4 w w PROPN ejpam-2219 212 5 klingenberg klingenberg PROPN ejpam-2219 212 6 . . PUNCT ejpam-2219 213 1 riemannian riemannian ADJ ejpam-2219 213 2 geometry geometry NOUN ejpam-2219 213 3 , , PUNCT ejpam-2219 213 4 volume volume NOUN ejpam-2219 213 5 1 1 NUM ejpam-2219 213 6 . . PUNCT ejpam-2219 213 7 walter walter PROPN ejpam-2219 213 8 de de PROPN ejpam-2219 213 9 gruyter gruyter PROPN ejpam-2219 213 10 , , PUNCT ejpam-2219 213 11 berlin berlin PROPN ejpam-2219 213 12 , , PUNCT ejpam-2219 213 13 new new PROPN ejpam-2219 213 14 york york PROPN ejpam-2219 213 15 , , PUNCT ejpam-2219 213 16 1995 1995 NUM ejpam-2219 213 17 . . PUNCT ejpam-2219 214 1 [ [ X ejpam-2219 214 2 23 23 NUM ejpam-2219 214 3 ] ] X ejpam-2219 214 4 k k PROPN ejpam-2219 214 5 konno konno PROPN ejpam-2219 214 6 and and CCONJ ejpam-2219 214 7 m m PROPN ejpam-2219 214 8 wadati wadati PROPN ejpam-2219 214 9 . . PUNCT ejpam-2219 215 1 simple simple ADJ ejpam-2219 215 2 derivation derivation NOUN ejpam-2219 215 3 of of ADP ejpam-2219 215 4 bäcklund bäcklund NOUN ejpam-2219 215 5 transformation transformation NOUN ejpam-2219 215 6 from from ADP ejpam-2219 215 7 riccati riccati PROPN ejpam-2219 215 8 form form NOUN ejpam-2219 215 9 of of ADP ejpam-2219 215 10 inverse inverse NOUN ejpam-2219 215 11 method method NOUN ejpam-2219 215 12 . . PUNCT ejpam-2219 216 1 progress progress NOUN ejpam-2219 216 2 of of ADP ejpam-2219 216 3 theoretical theoretical ADJ ejpam-2219 216 4 physics physics NOUN ejpam-2219 216 5 , , PUNCT ejpam-2219 216 6 53(6):1652–1656 53(6):1652–1656 NUM ejpam-2219 216 7 , , PUNCT ejpam-2219 216 8 1975 1975 NUM ejpam-2219 216 9 . . PUNCT ejpam-2219 217 1 references reference NOUN ejpam-2219 217 2 573 573 NUM ejpam-2219 217 3 [ [ X ejpam-2219 217 4 24 24 NUM ejpam-2219 217 5 ] ] X ejpam-2219 217 6 e e NOUN ejpam-2219 217 7 reyes reyes PROPN ejpam-2219 217 8 . . PUNCT ejpam-2219 218 1 conservation conservation NOUN ejpam-2219 218 2 laws law NOUN ejpam-2219 218 3 and and CCONJ ejpam-2219 218 4 calapso calapso ADJ ejpam-2219 218 5 - - PUNCT ejpam-2219 218 6 guichard guichard NOUN ejpam-2219 218 7 deformations deformation NOUN ejpam-2219 218 8 of of ADP ejpam-2219 218 9 equations equation NOUN ejpam-2219 218 10 describing describe VERB ejpam-2219 218 11 pseudo pseudo NOUN ejpam-2219 218 12 - - ADJ ejpam-2219 218 13 spherical spherical ADJ ejpam-2219 218 14 surfaces surface NOUN ejpam-2219 218 15 . . PUNCT ejpam-2219 219 1 journal journal NOUN ejpam-2219 219 2 of of ADP ejpam-2219 219 3 mathematical mathematical ADJ ejpam-2219 219 4 physics physics NOUN ejpam-2219 219 5 , , PUNCT ejpam-2219 219 6 41(5):2968–2989 41(5):2968–2989 NUM ejpam-2219 219 7 , , PUNCT ejpam-2219 219 8 2000 2000 NUM ejpam-2219 219 9 . . PUNCT ejpam-2219 220 1 [ [ X ejpam-2219 220 2 25 25 NUM ejpam-2219 220 3 ] ] X ejpam-2219 220 4 e e NOUN ejpam-2219 220 5 reyes reyes PROPN ejpam-2219 220 6 . . PUNCT ejpam-2219 221 1 on on ADP ejpam-2219 221 2 geometrically geometrically ADV ejpam-2219 221 3 integrable integrable ADJ ejpam-2219 221 4 equations equation NOUN ejpam-2219 221 5 and and CCONJ ejpam-2219 221 6 hierarchies hierarchy NOUN ejpam-2219 221 7 of of ADP ejpam-2219 221 8 pseudo pseudo NOUN ejpam-2219 221 9 - - ADJ ejpam-2219 221 10 spherical spherical ADJ ejpam-2219 221 11 type type NOUN ejpam-2219 221 12 . . PUNCT ejpam-2219 222 1 contemporary contemporary ADJ ejpam-2219 222 2 mathematics mathematics PROPN ejpam-2219 222 3 , , PUNCT ejpam-2219 222 4 285:145–156 285:145–156 NUM ejpam-2219 222 5 , , PUNCT ejpam-2219 222 6 2001 2001 NUM ejpam-2219 222 7 . . PUNCT ejpam-2219 223 1 [ [ X ejpam-2219 223 2 26 26 NUM ejpam-2219 223 3 ] ] X ejpam-2219 223 4 r r NOUN ejpam-2219 223 5 sasaki sasaki NOUN ejpam-2219 223 6 . . PUNCT ejpam-2219 224 1 soliton soliton NOUN ejpam-2219 224 2 equations equation NOUN ejpam-2219 224 3 and and CCONJ ejpam-2219 224 4 pseudospherical pseudospherical ADJ ejpam-2219 224 5 surfaces surface NOUN ejpam-2219 224 6 . . PUNCT ejpam-2219 225 1 nuclear nuclear ADJ ejpam-2219 225 2 physics physics PROPN ejpam-2219 225 3 b b PROPN ejpam-2219 225 4 , , PUNCT ejpam-2219 225 5 154(2):343–357 154(2):343–357 PROPN ejpam-2219 225 6 , , PUNCT ejpam-2219 225 7 1979 1979 NUM ejpam-2219 225 8 . . PUNCT ejpam-2219 226 1 [ [ X ejpam-2219 226 2 27 27 NUM ejpam-2219 226 3 ] ] X ejpam-2219 226 4 s s AUX ejpam-2219 226 5 sayed say VERB ejpam-2219 226 6 and and CCONJ ejpam-2219 226 7 g g PROPN ejpam-2219 226 8 gharib gharib PROPN ejpam-2219 226 9 . . PUNCT ejpam-2219 227 1 canonical canonical ADJ ejpam-2219 227 2 reduction reduction NOUN ejpam-2219 227 3 of of ADP ejpam-2219 227 4 self self NOUN ejpam-2219 227 5 - - PUNCT ejpam-2219 227 6 dual dual ADJ ejpam-2219 227 7 yang yang PROPN ejpam-2219 227 8 – – PUNCT ejpam-2219 227 9 mills mill NOUN ejpam-2219 227 10 equations equation NOUN ejpam-2219 227 11 to to PART ejpam-2219 227 12 fitzhugh fitzhugh VERB ejpam-2219 227 13 – – PUNCT ejpam-2219 227 14 nagumo nagumo ADJ ejpam-2219 227 15 equation equation NOUN ejpam-2219 227 16 and and CCONJ ejpam-2219 227 17 exact exact ADJ ejpam-2219 227 18 solutions solution NOUN ejpam-2219 227 19 . . PUNCT ejpam-2219 228 1 chaos chaos NOUN ejpam-2219 228 2 , , PUNCT ejpam-2219 228 3 solitons soliton NOUN ejpam-2219 228 4 & & CCONJ ejpam-2219 228 5 fractals fractal NOUN ejpam-2219 228 6 , , PUNCT ejpam-2219 228 7 39(2):492 39(2):492 NUM ejpam-2219 228 8 – – PUNCT ejpam-2219 228 9 498 498 NUM ejpam-2219 228 10 , , PUNCT ejpam-2219 228 11 2009 2009 NUM ejpam-2219 228 12 . . PUNCT ejpam-2219 229 1 [ [ X ejpam-2219 229 2 28 28 NUM ejpam-2219 229 3 ] ] X ejpam-2219 229 4 e e X ejpam-2219 229 5 witten witten PROPN ejpam-2219 229 6 . . PUNCT ejpam-2219 230 1 two two NUM ejpam-2219 230 2 - - PUNCT ejpam-2219 230 3 dimensional dimensional ADJ ejpam-2219 230 4 gravity gravity NOUN ejpam-2219 230 5 and and CCONJ ejpam-2219 230 6 intersection intersection NOUN ejpam-2219 230 7 theory theory NOUN ejpam-2219 230 8 on on ADP ejpam-2219 230 9 moduli modulus NOUN ejpam-2219 230 10 space space NOUN ejpam-2219 230 11 . . PUNCT ejpam-2219 231 1 surveys survey NOUN ejpam-2219 231 2 in in ADP ejpam-2219 231 3 differential differential ADJ ejpam-2219 231 4 geometry geometry NOUN ejpam-2219 231 5 , , PUNCT ejpam-2219 231 6 1(243):74 1(243):74 NUM ejpam-2219 231 7 , , PUNCT ejpam-2219 231 8 1991 1991 NUM ejpam-2219 231 9 . . PUNCT ejpam-2219 232 1 [ [ X ejpam-2219 232 2 29 29 NUM ejpam-2219 232 3 ] ] X ejpam-2219 232 4 c c PROPN ejpam-2219 232 5 yang yang PROPN ejpam-2219 232 6 and and CCONJ ejpam-2219 232 7 r r NOUN ejpam-2219 232 8 mills mill NOUN ejpam-2219 232 9 . . PUNCT ejpam-2219 233 1 conservation conservation NOUN ejpam-2219 233 2 of of ADP ejpam-2219 233 3 isotopic isotopic ADJ ejpam-2219 233 4 spin spin NOUN ejpam-2219 233 5 and and CCONJ ejpam-2219 233 6 isotopic isotopic ADJ ejpam-2219 233 7 gauge gauge NOUN ejpam-2219 233 8 invariance invariance NOUN ejpam-2219 233 9 . . PUNCT ejpam-2219 234 1 physical physical ADJ ejpam-2219 234 2 review review NOUN ejpam-2219 234 3 , , PUNCT ejpam-2219 234 4 96(1):191–195 96(1):191–195 PROPN ejpam-2219 234 5 , , PUNCT ejpam-2219 234 6 1954 1954 NUM ejpam-2219 234 7 . . PUNCT