id	sid	tid	token	lemma	pos
cana-934	1	1	communications	communication	NOUN
cana-934	1	2	on	on	ADP
cana-934	1	3	applied	apply	VERB
cana-934	1	4	nonlinear	nonlinear	ADJ
cana-934	1	5	analysis	analysis	NOUN
cana-934	1	6	issn	issn	NOUN
cana-934	1	7	:	:	PUNCT
cana-934	1	8	1074	1074	NUM
cana-934	1	9	-	-	PUNCT
cana-934	1	10	133x	133x	NUM
cana-934	1	11	vol	vol	NOUN
cana-934	1	12	31	31	NUM
cana-934	1	13	no	no	NOUN
cana-934	1	14	.	.	PUNCT
cana-934	2	1	4s	4s	NUM
cana-934	2	2	(	(	PUNCT
cana-934	2	3	2024	2024	NUM
cana-934	2	4	)	)	PUNCT
cana-934	2	5	410	410	NUM
cana-934	3	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-934	3	2	analysis	analysis	NOUN
cana-934	3	3	of	of	ADP
cana-934	3	4	nonlinear	nonlinear	ADJ
cana-934	3	5	schrödinger	schrödinger	ADJ
cana-934	3	6	equations	equation	NOUN
cana-934	3	7	with	with	ADP
cana-934	3	8	time	time	NOUN
cana-934	3	9	-	-	PUNCT
cana-934	3	10	dependent	dependent	ADJ
cana-934	3	11	coefficients	coefficient	NOUN
cana-934	3	12	:	:	PUNCT
cana-934	3	13	stability	stability	NOUN
cana-934	3	14	and	and	CCONJ
cana-934	3	15	decay	decay	NOUN
cana-934	3	16	properties	property	NOUN
cana-934	3	17	dr	dr	PROPN
cana-934	3	18	.	.	PROPN
cana-934	3	19	eric	eric	PROPN
cana-934	3	20	howard1	howard1	PROPN
cana-934	3	21	,	,	PUNCT
cana-934	3	22	dr	dr	PROPN
cana-934	3	23	nand	nand	PROPN
cana-934	3	24	kumar2	kumar2	PROPN
cana-934	3	25	1	1	NUM
cana-934	3	26	department	department	PROPN
cana-934	3	27	of	of	ADP
cana-934	3	28	physics	physics	PROPN
cana-934	3	29	and	and	CCONJ
cana-934	3	30	astronomy	astronomy	NOUN
cana-934	3	31	,	,	PUNCT
cana-934	3	32	macquarie	macquarie	PROPN
cana-934	3	33	university	university	PROPN
cana-934	3	34	,	,	PUNCT
cana-934	3	35	australia	australia	PROPN
cana-934	3	36	.	.	PUNCT
cana-934	4	1	email	email	NOUN
cana-934	5	1	i	i	PROPN
cana-934	5	2	d	d	PROPN
cana-934	5	3	eric.howard@mq.edu.au	eric.howard@mq.edu.au	PROPN
cana-934	5	4	.	.	PUNCT
cana-934	6	1	orcid	orcid	NOUN
cana-934	6	2	:	:	PUNCT
cana-934	6	3	0000	0000	NUM
cana-934	6	4	-	-	PUNCT
cana-934	6	5	0002	0002	NUM
cana-934	6	6	-	-	PUNCT
cana-934	6	7	8133	8133	NUM
cana-934	6	8	-	-	PUNCT
cana-934	6	9	8323	8323	NUM
cana-934	6	10	.	.	PUNCT
cana-934	7	1	2	2	NUM
cana-934	7	2	assistant	assistant	NOUN
cana-934	7	3	professor	professor	NOUN
cana-934	7	4	,	,	PUNCT
cana-934	7	5	department	department	PROPN
cana-934	7	6	of	of	ADP
cana-934	7	7	physics	physics	PROPN
cana-934	7	8	jawaharlal	jawaharlal	PROPN
cana-934	7	9	nehru	nehru	PROPN
cana-934	7	10	memorial	memorial	PROPN
cana-934	7	11	pg	pg	PROPN
cana-934	7	12	college	college	PROPN
cana-934	7	13	,	,	PUNCT
cana-934	7	14	barabanki	barabanki	PROPN
cana-934	7	15	,	,	PUNCT
cana-934	7	16	up	up	ADP
cana-934	7	17	,	,	PUNCT
cana-934	7	18	india	india	PROPN
cana-934	7	19	.email:nandkumar350@gmail.com	.email:nandkumar350@gmail.com	PROPN
cana-934	7	20	.	.	PUNCT
cana-934	8	1	orcid	orcid	NOUN
cana-934	8	2	:	:	PUNCT
cana-934	8	3	0009	0009	NUM
cana-934	8	4	-	-	SYM
cana-934	8	5	0004	0004	NUM
cana-934	8	6	-	-	PUNCT
cana-934	8	7	3139	3139	NUM
cana-934	8	8	-	-	PUNCT
cana-934	8	9	3385	3385	NUM
cana-934	8	10	article	article	NOUN
cana-934	8	11	history	history	NOUN
cana-934	8	12	:	:	PUNCT
cana-934	8	13	received	receive	VERB
cana-934	8	14	:	:	PUNCT
cana-934	8	15	18	18	NUM
cana-934	8	16	-	-	PUNCT
cana-934	8	17	04	04	NUM
cana-934	8	18	-	-	PUNCT
cana-934	8	19	2024	2024	NUM
cana-934	8	20	revised	revise	VERB
cana-934	8	21	:	:	PUNCT
cana-934	8	22	10	10	NUM
cana-934	8	23	-	-	SYM
cana-934	8	24	06	06	NUM
cana-934	8	25	-	-	PUNCT
cana-934	8	26	2024	2024	NUM
cana-934	8	27	accepted	accept	VERB
cana-934	8	28	:	:	PUNCT
cana-934	8	29	23	23	NUM
cana-934	8	30	-	-	SYM
cana-934	8	31	06	06	NUM
cana-934	8	32	-	-	PUNCT
cana-934	8	33	2024	2024	NUM
cana-934	8	34	abstract	abstract	NOUN
cana-934	8	35	:	:	PUNCT
cana-934	8	36	this	this	DET
cana-934	8	37	study	study	NOUN
cana-934	8	38	investigates	investigate	VERB
cana-934	8	39	the	the	DET
cana-934	8	40	stability	stability	NOUN
cana-934	8	41	and	and	CCONJ
cana-934	8	42	decay	decay	NOUN
cana-934	8	43	properties	property	NOUN
cana-934	8	44	of	of	ADP
cana-934	8	45	solutions	solution	NOUN
cana-934	8	46	to	to	PART
cana-934	8	47	nonlinear	nonlinear	VERB
cana-934	8	48	schrödinger	schrödinger	ADJ
cana-934	8	49	equations	equation	NOUN
cana-934	8	50	(	(	PUNCT
cana-934	8	51	nlses	nlse	NOUN
cana-934	8	52	)	)	PUNCT
cana-934	8	53	with	with	ADP
cana-934	8	54	time	time	NOUN
cana-934	8	55	-	-	PUNCT
cana-934	8	56	dependent	dependent	ADJ
cana-934	8	57	coefficients	coefficient	NOUN
cana-934	8	58	.	.	PUNCT
cana-934	9	1	employing	employ	VERB
cana-934	9	2	a	a	DET
cana-934	9	3	blend	blend	NOUN
cana-934	9	4	of	of	ADP
cana-934	9	5	analytical	analytical	ADJ
cana-934	9	6	and	and	CCONJ
cana-934	9	7	numerical	numerical	ADJ
cana-934	9	8	methods	method	NOUN
cana-934	9	9	,	,	PUNCT
cana-934	9	10	we	we	PRON
cana-934	9	11	delve	delve	VERB
cana-934	9	12	into	into	ADP
cana-934	9	13	how	how	SCONJ
cana-934	9	14	temporal	temporal	ADJ
cana-934	9	15	variations	variation	NOUN
cana-934	9	16	in	in	ADP
cana-934	9	17	coefficients	coefficient	NOUN
cana-934	9	18	influence	influence	VERB
cana-934	9	19	the	the	DET
cana-934	9	20	dynamics	dynamic	NOUN
cana-934	9	21	of	of	ADP
cana-934	9	22	wave	wave	NOUN
cana-934	9	23	functions	function	NOUN
cana-934	9	24	.	.	PUNCT
cana-934	10	1	our	our	PRON
cana-934	10	2	analysis	analysis	NOUN
cana-934	10	3	reveals	reveal	VERB
cana-934	10	4	that	that	SCONJ
cana-934	10	5	time	time	NOUN
cana-934	10	6	-	-	PUNCT
cana-934	10	7	dependent	dependent	ADJ
cana-934	10	8	coefficients	coefficient	NOUN
cana-934	10	9	significantly	significantly	ADV
cana-934	10	10	affect	affect	VERB
cana-934	10	11	the	the	DET
cana-934	10	12	stability	stability	NOUN
cana-934	10	13	and	and	CCONJ
cana-934	10	14	decay	decay	NOUN
cana-934	10	15	rates	rate	NOUN
cana-934	10	16	of	of	ADP
cana-934	10	17	solutions	solution	NOUN
cana-934	10	18	,	,	PUNCT
cana-934	10	19	uncovering	uncover	VERB
cana-934	10	20	conditions	condition	NOUN
cana-934	10	21	that	that	PRON
cana-934	10	22	lead	lead	VERB
cana-934	10	23	to	to	ADP
cana-934	10	24	either	either	CCONJ
cana-934	10	25	enhanced	enhance	VERB
cana-934	10	26	stability	stability	NOUN
cana-934	10	27	or	or	CCONJ
cana-934	10	28	accelerated	accelerate	VERB
cana-934	10	29	decay	decay	NOUN
cana-934	10	30	.	.	PUNCT
cana-934	11	1	the	the	DET
cana-934	11	2	findings	finding	NOUN
cana-934	11	3	highlight	highlight	VERB
cana-934	11	4	the	the	DET
cana-934	11	5	critical	critical	ADJ
cana-934	11	6	role	role	NOUN
cana-934	11	7	of	of	ADP
cana-934	11	8	coefficient	coefficient	NOUN
cana-934	11	9	temporality	temporality	NOUN
cana-934	11	10	in	in	ADP
cana-934	11	11	dictating	dictate	VERB
cana-934	11	12	the	the	DET
cana-934	11	13	behavior	behavior	NOUN
cana-934	11	14	of	of	ADP
cana-934	11	15	nlse	nlse	ADJ
cana-934	11	16	solutions	solution	NOUN
cana-934	11	17	.	.	PUNCT
cana-934	12	1	these	these	DET
cana-934	12	2	insights	insight	NOUN
cana-934	12	3	not	not	PART
cana-934	12	4	only	only	ADV
cana-934	12	5	advance	advance	VERB
cana-934	12	6	our	our	PRON
cana-934	12	7	theoretical	theoretical	ADJ
cana-934	12	8	understanding	understanding	NOUN
cana-934	12	9	of	of	ADP
cana-934	12	10	nlses	nlse	NOUN
cana-934	12	11	but	but	CCONJ
cana-934	12	12	also	also	ADV
cana-934	12	13	bear	bear	VERB
cana-934	12	14	implications	implication	NOUN
cana-934	12	15	for	for	ADP
cana-934	12	16	practical	practical	ADJ
cana-934	12	17	applications	application	NOUN
cana-934	12	18	in	in	ADP
cana-934	12	19	fields	field	NOUN
cana-934	12	20	modeled	model	VERB
cana-934	12	21	by	by	ADP
cana-934	12	22	these	these	DET
cana-934	12	23	equations	equation	NOUN
cana-934	12	24	.	.	PUNCT
cana-934	13	1	our	our	PRON
cana-934	13	2	research	research	NOUN
cana-934	13	3	opens	open	VERB
cana-934	13	4	avenues	avenue	NOUN
cana-934	13	5	for	for	ADP
cana-934	13	6	exploiting	exploit	VERB
cana-934	13	7	time	time	NOUN
cana-934	13	8	-	-	PUNCT
cana-934	13	9	dependent	dependent	ADJ
cana-934	13	10	behaviors	behavior	NOUN
cana-934	13	11	in	in	ADP
cana-934	13	12	designing	design	VERB
cana-934	13	13	systems	system	NOUN
cana-934	13	14	with	with	ADP
cana-934	13	15	desired	desire	VERB
cana-934	13	16	dynamical	dynamical	ADJ
cana-934	13	17	properties	property	NOUN
cana-934	13	18	.	.	PUNCT
cana-934	14	1	keywords	keyword	NOUN
cana-934	14	2	:	:	PUNCT
cana-934	14	3	quantum	quantum	ADJ
cana-934	14	4	noise	noise	NOUN
cana-934	14	5	-	-	PUNCT
cana-934	14	6	extended	extend	VERB
cana-934	14	7	nonlinear	nonlinear	ADJ
cana-934	14	8	schrödinger	schrödinger	ADJ
cana-934	14	9	equation	equation	NOUN
cana-934	14	10	,	,	PUNCT
cana-934	14	11	quantum	quantum	NOUN
cana-934	14	12	chaos	chaos	NOUN
cana-934	14	13	,	,	PUNCT
cana-934	14	14	soliton	soliton	NOUN
cana-934	14	15	dynamics	dynamic	NOUN
cana-934	14	16	,	,	PUNCT
cana-934	14	17	quantum	quantum	ADJ
cana-934	14	18	turbulence	turbulence	NOUN
cana-934	14	19	,	,	PUNCT
cana-934	14	20	multi	multi	ADJ
cana-934	14	21	-	-	ADJ
cana-934	14	22	particle	particle	ADJ
cana-934	14	23	interactions	interaction	NOUN
cana-934	14	24	,	,	PUNCT
cana-934	14	25	stability	stability	NOUN
cana-934	14	26	and	and	CCONJ
cana-934	14	27	decay	decay	NOUN
cana-934	14	28	properties	property	NOUN
cana-934	14	29	,	,	PUNCT
cana-934	14	30	quantum	quantum	NOUN
cana-934	14	31	computing	computing	NOUN
cana-934	14	32	applications	application	NOUN
cana-934	14	33	,	,	PUNCT
cana-934	14	34	nonlinear	nonlinear	ADJ
cana-934	14	35	quantum	quantum	ADJ
cana-934	14	36	systems	system	NOUN
cana-934	14	37	,	,	PUNCT
cana-934	14	38	quantum	quantum	ADJ
cana-934	14	39	vortex	vortex	NOUN
cana-934	14	40	dynamics	dynamic	NOUN
cana-934	14	41	.	.	PUNCT
cana-934	15	1	1	1	X
cana-934	15	2	.	.	X
cana-934	15	3	introduction	introduction	NOUN
cana-934	15	4	the	the	DET
cana-934	15	5	genesis	genesis	NOUN
cana-934	15	6	of	of	ADP
cana-934	15	7	the	the	DET
cana-934	15	8	nonlinear	nonlinear	ADJ
cana-934	15	9	schrödinger	schrödinger	ADJ
cana-934	15	10	equation	equation	NOUN
cana-934	15	11	(	(	PUNCT
cana-934	15	12	nlse	nlse	ADJ
cana-934	15	13	)	)	PUNCT
cana-934	15	14	traces	trace	VERB
cana-934	15	15	back	back	ADV
cana-934	15	16	to	to	ADP
cana-934	15	17	the	the	DET
cana-934	15	18	early	early	ADJ
cana-934	15	19	20th	20th	ADJ
cana-934	15	20	century	century	NOUN
cana-934	15	21	,	,	PUNCT
cana-934	15	22	marking	mark	VERB
cana-934	15	23	a	a	DET
cana-934	15	24	significant	significant	ADJ
cana-934	15	25	milestone	milestone	NOUN
cana-934	15	26	in	in	ADP
cana-934	15	27	the	the	DET
cana-934	15	28	evolution	evolution	NOUN
cana-934	15	29	of	of	ADP
cana-934	15	30	quantum	quantum	ADJ
cana-934	15	31	mechanics	mechanic	NOUN
cana-934	15	32	and	and	CCONJ
cana-934	15	33	nonlinear	nonlinear	ADJ
cana-934	15	34	dynamics	dynamic	NOUN
cana-934	15	35	.	.	PUNCT
cana-934	16	1	initially	initially	ADV
cana-934	16	2	conceptualized	conceptualize	VERB
cana-934	16	3	to	to	PART
cana-934	16	4	model	model	VERB
cana-934	16	5	the	the	DET
cana-934	16	6	behavior	behavior	NOUN
cana-934	16	7	of	of	ADP
cana-934	16	8	quantum	quantum	ADJ
cana-934	16	9	particles	particle	NOUN
cana-934	16	10	,	,	PUNCT
cana-934	16	11	the	the	DET
cana-934	16	12	nlse	nlse	NOUN
cana-934	16	13	rapidly	rapidly	ADV
cana-934	16	14	found	find	VERB
cana-934	16	15	utility	utility	NOUN
cana-934	16	16	across	across	ADP
cana-934	16	17	a	a	DET
cana-934	16	18	spectrum	spectrum	NOUN
cana-934	16	19	of	of	ADP
cana-934	16	20	disciplines	discipline	NOUN
cana-934	16	21	,	,	PUNCT
cana-934	16	22	from	from	ADP
cana-934	16	23	optics	optic	NOUN
cana-934	16	24	and	and	CCONJ
cana-934	16	25	photonics	photonic	NOUN
cana-934	16	26	to	to	ADP
cana-934	16	27	fluid	fluid	ADJ
cana-934	16	28	dynamics	dynamic	NOUN
cana-934	16	29	and	and	CCONJ
cana-934	16	30	beyond	beyond	ADP
cana-934	16	31	.	.	PUNCT
cana-934	17	1	characterized	characterize	VERB
cana-934	17	2	by	by	ADP
cana-934	17	3	its	its	PRON
cana-934	17	4	ability	ability	NOUN
cana-934	17	5	to	to	PART
cana-934	17	6	describe	describe	VERB
cana-934	17	7	the	the	DET
cana-934	17	8	propagation	propagation	NOUN
cana-934	17	9	of	of	ADP
cana-934	17	10	waves	wave	NOUN
cana-934	17	11	in	in	ADP
cana-934	17	12	nonlinear	nonlinear	ADJ
cana-934	17	13	media	medium	NOUN
cana-934	17	14	,	,	PUNCT
cana-934	17	15	the	the	DET
cana-934	17	16	equation	equation	NOUN
cana-934	17	17	serves	serve	VERB
cana-934	17	18	as	as	ADP
cana-934	17	19	a	a	DET
cana-934	17	20	fundamental	fundamental	ADJ
cana-934	17	21	tool	tool	NOUN
cana-934	17	22	in	in	ADP
cana-934	17	23	understanding	understand	VERB
cana-934	17	24	phenomena	phenomenon	NOUN
cana-934	17	25	such	such	ADJ
cana-934	17	26	as	as	ADP
cana-934	17	27	soliton	soliton	NOUN
cana-934	17	28	formation	formation	NOUN
cana-934	17	29	,	,	PUNCT
cana-934	17	30	wave	wave	NOUN
cana-934	17	31	packet	packet	NOUN
cana-934	17	32	dispersion	dispersion	NOUN
cana-934	17	33	,	,	PUNCT
cana-934	17	34	and	and	CCONJ
cana-934	17	35	the	the	DET
cana-934	17	36	intricate	intricate	ADJ
cana-934	17	37	balance	balance	NOUN
cana-934	17	38	between	between	ADP
cana-934	17	39	nonlinearity	nonlinearity	NOUN
cana-934	17	40	and	and	CCONJ
cana-934	17	41	dispersion	dispersion	NOUN
cana-934	17	42	.	.	PUNCT
cana-934	18	1	motivation	motivation	NOUN
cana-934	18	2	for	for	ADP
cana-934	18	3	extending	extend	VERB
cana-934	18	4	the	the	DET
cana-934	18	5	nlse	nlse	NOUN
cana-934	18	6	despite	despite	SCONJ
cana-934	18	7	the	the	DET
cana-934	18	8	profound	profound	ADJ
cana-934	18	9	insights	insight	NOUN
cana-934	18	10	offered	offer	VERB
cana-934	18	11	by	by	ADP
cana-934	18	12	the	the	DET
cana-934	18	13	classical	classical	ADJ
cana-934	18	14	nlse	nlse	NOUN
cana-934	18	15	,	,	PUNCT
cana-934	18	16	its	its	PRON
cana-934	18	17	application	application	NOUN
cana-934	18	18	is	be	AUX
cana-934	18	19	predominantly	predominantly	ADV
cana-934	18	20	confined	confine	VERB
cana-934	18	21	to	to	ADP
cana-934	18	22	scenarios	scenario	NOUN
cana-934	18	23	assuming	assume	VERB
cana-934	18	24	constant	constant	ADJ
cana-934	18	25	or	or	CCONJ
cana-934	18	26	linear	linear	ADJ
cana-934	18	27	coefficients	coefficient	NOUN
cana-934	18	28	,	,	PUNCT
cana-934	18	29	limiting	limit	VERB
cana-934	18	30	its	its	PRON
cana-934	18	31	portrayal	portrayal	NOUN
cana-934	18	32	of	of	ADP
cana-934	18	33	more	more	ADJ
cana-934	18	34	complex	complex	ADJ
cana-934	18	35	systems	system	NOUN
cana-934	18	36	where	where	SCONJ
cana-934	18	37	these	these	DET
cana-934	18	38	coefficients	coefficient	NOUN
cana-934	18	39	vary	vary	VERB
cana-934	18	40	with	with	ADP
cana-934	18	41	time	time	NOUN
cana-934	18	42	.	.	PUNCT
cana-934	19	1	this	this	DET
cana-934	19	2	restriction	restriction	NOUN
cana-934	19	3	overlooks	overlook	VERB
cana-934	19	4	the	the	DET
cana-934	19	5	dynamic	dynamic	ADJ
cana-934	19	6	nature	nature	NOUN
cana-934	19	7	of	of	ADP
cana-934	19	8	many	many	ADJ
cana-934	19	9	physical	physical	ADJ
cana-934	19	10	and	and	CCONJ
cana-934	19	11	quantum	quantum	NOUN
cana-934	19	12	systems	system	NOUN
cana-934	19	13	,	,	PUNCT
cana-934	19	14	where	where	SCONJ
cana-934	19	15	time	time	NOUN
cana-934	19	16	-	-	PUNCT
cana-934	19	17	dependent	dependent	ADJ
cana-934	19	18	changes	change	NOUN
cana-934	19	19	in	in	ADP
cana-934	19	20	the	the	DET
cana-934	19	21	environment	environment	NOUN
cana-934	19	22	or	or	CCONJ
cana-934	19	23	in	in	ADP
cana-934	19	24	the	the	DET
cana-934	19	25	system	system	NOUN
cana-934	19	26	itself	itself	PRON
cana-934	19	27	can	can	AUX
cana-934	19	28	significantly	significantly	ADV
cana-934	19	29	influence	influence	VERB
cana-934	19	30	the	the	DET
cana-934	19	31	behavior	behavior	NOUN
cana-934	19	32	of	of	ADP
cana-934	19	33	wave	wave	NOUN
cana-934	19	34	functions	function	NOUN
cana-934	19	35	.	.	PUNCT
cana-934	20	1	consequently	consequently	ADV
cana-934	20	2	,	,	PUNCT
cana-934	20	3	there	there	PRON
cana-934	20	4	exists	exist	VERB
cana-934	20	5	a	a	DET
cana-934	20	6	pressing	press	VERB
cana-934	20	7	need	need	NOUN
cana-934	20	8	to	to	PART
cana-934	20	9	extend	extend	VERB
cana-934	20	10	the	the	DET
cana-934	20	11	classical	classical	ADJ
cana-934	20	12	nlse	nlse	ADJ
cana-934	20	13	framework	framework	NOUN
cana-934	20	14	to	to	PART
cana-934	20	15	encompass	encompass	VERB
cana-934	20	16	time	time	NOUN
cana-934	20	17	-	-	PUNCT
cana-934	20	18	dependent	dependent	ADJ
cana-934	20	19	coefficients	coefficient	NOUN
cana-934	20	20	,	,	PUNCT
cana-934	20	21	thereby	thereby	ADV
cana-934	20	22	enhancing	enhance	VERB
cana-934	20	23	its	its	PRON
cana-934	20	24	descriptive	descriptive	ADJ
cana-934	20	25	power	power	NOUN
cana-934	20	26	and	and	CCONJ
cana-934	20	27	applicability	applicability	NOUN
cana-934	20	28	to	to	ADP
cana-934	20	29	a	a	DET
cana-934	20	30	broader	broad	ADJ
cana-934	20	31	range	range	NOUN
cana-934	20	32	of	of	ADP
cana-934	20	33	phenomena	phenomenon	NOUN
cana-934	20	34	.	.	PUNCT
cana-934	21	1	this	this	DET
cana-934	21	2	extension	extension	NOUN
cana-934	21	3	is	be	AUX
cana-934	21	4	crucial	crucial	ADJ
cana-934	21	5	for	for	ADP
cana-934	21	6	accurately	accurately	ADV
cana-934	21	7	modeling	model	VERB
cana-934	21	8	systems	system	NOUN
cana-934	21	9	subject	subject	ADJ
cana-934	21	10	to	to	ADP
cana-934	21	11	temporal	temporal	ADJ
cana-934	21	12	variations	variation	NOUN
cana-934	21	13	,	,	PUNCT
cana-934	21	14	including	include	VERB
cana-934	21	15	but	but	CCONJ
cana-934	21	16	not	not	PART
cana-934	21	17	limited	limit	VERB
cana-934	21	18	to	to	ADP
cana-934	21	19	,	,	PUNCT
cana-934	21	20	communications	communication	NOUN
cana-934	21	21	on	on	ADP
cana-934	21	22	applied	apply	VERB
cana-934	21	23	nonlinear	nonlinear	ADJ
cana-934	21	24	analysis	analysis	NOUN
cana-934	21	25	issn	issn	NOUN
cana-934	21	26	:	:	PUNCT
cana-934	21	27	1074	1074	NUM
cana-934	21	28	-	-	PUNCT
cana-934	21	29	133x	133x	NUM
cana-934	21	30	vol	vol	NOUN
cana-934	21	31	31	31	NUM
cana-934	21	32	no	no	NOUN
cana-934	21	33	.	.	PUNCT
cana-934	22	1	4s	4s	NUM
cana-934	22	2	(	(	PUNCT
cana-934	22	3	2024	2024	NUM
cana-934	22	4	)	)	PUNCT
cana-934	22	5	411	411	NUM
cana-934	22	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-934	22	7	changing	change	VERB
cana-934	22	8	refractive	refractive	ADJ
cana-934	22	9	indices	index	NOUN
cana-934	22	10	in	in	ADP
cana-934	22	11	nonlinear	nonlinear	ADJ
cana-934	22	12	optics	optic	NOUN
cana-934	22	13	,	,	PUNCT
cana-934	22	14	time	time	NOUN
cana-934	22	15	-	-	PUNCT
cana-934	22	16	varying	vary	VERB
cana-934	22	17	potentials	potential	NOUN
cana-934	22	18	in	in	ADP
cana-934	22	19	quantum	quantum	ADJ
cana-934	22	20	wells	well	NOUN
cana-934	22	21	,	,	PUNCT
cana-934	22	22	and	and	CCONJ
cana-934	22	23	evolving	evolve	VERB
cana-934	22	24	environmental	environmental	ADJ
cana-934	22	25	conditions	condition	NOUN
cana-934	22	26	in	in	ADP
cana-934	22	27	fluid	fluid	ADJ
cana-934	22	28	systems	system	NOUN
cana-934	22	29	.	.	PUNCT
cana-934	23	1	objectives	objective	VERB
cana-934	23	2	the	the	DET
cana-934	23	3	primary	primary	ADJ
cana-934	23	4	aim	aim	NOUN
cana-934	23	5	of	of	ADP
cana-934	23	6	this	this	DET
cana-934	23	7	research	research	NOUN
cana-934	23	8	is	be	AUX
cana-934	23	9	to	to	PART
cana-934	23	10	bridge	bridge	VERB
cana-934	23	11	the	the	DET
cana-934	23	12	gap	gap	NOUN
cana-934	23	13	left	leave	VERB
cana-934	23	14	by	by	ADP
cana-934	23	15	the	the	DET
cana-934	23	16	classical	classical	ADJ
cana-934	23	17	nlse	nlse	NOUN
cana-934	23	18	by	by	ADP
cana-934	23	19	introducing	introduce	VERB
cana-934	23	20	and	and	CCONJ
cana-934	23	21	analyzing	analyze	VERB
cana-934	23	22	a	a	DET
cana-934	23	23	modified	modify	VERB
cana-934	23	24	version	version	NOUN
cana-934	23	25	that	that	PRON
cana-934	23	26	incorporates	incorporate	VERB
cana-934	23	27	time	time	NOUN
cana-934	23	28	-	-	PUNCT
cana-934	23	29	dependent	dependent	ADJ
cana-934	23	30	coefficients	coefficient	NOUN
cana-934	23	31	.	.	PUNCT
cana-934	24	1	through	through	ADP
cana-934	24	2	this	this	DET
cana-934	24	3	endeavor	endeavor	NOUN
cana-934	24	4	,	,	PUNCT
cana-934	24	5	we	we	PRON
cana-934	24	6	seek	seek	VERB
cana-934	24	7	to	to	PART
cana-934	24	8	:	:	PUNCT
cana-934	24	9	1	1	X
cana-934	24	10	.	.	X
cana-934	24	11	characterize	characterize	VERB
cana-934	24	12	the	the	DET
cana-934	24	13	stability	stability	NOUN
cana-934	24	14	properties	property	NOUN
cana-934	24	15	:	:	PUNCT
cana-934	24	16	determine	determine	VERB
cana-934	24	17	how	how	SCONJ
cana-934	24	18	the	the	DET
cana-934	24	19	introduction	introduction	NOUN
cana-934	24	20	of	of	ADP
cana-934	24	21	time	time	NOUN
cana-934	24	22	-	-	PUNCT
cana-934	24	23	dependent	dependent	ADJ
cana-934	24	24	coefficients	coefficient	NOUN
cana-934	24	25	influences	influence	VERB
cana-934	24	26	the	the	DET
cana-934	24	27	stability	stability	NOUN
cana-934	24	28	of	of	ADP
cana-934	24	29	wave	wave	NOUN
cana-934	24	30	functions	function	NOUN
cana-934	24	31	,	,	PUNCT
cana-934	24	32	identifying	identify	VERB
cana-934	24	33	conditions	condition	NOUN
cana-934	24	34	under	under	ADP
cana-934	24	35	which	which	PRON
cana-934	24	36	these	these	DET
cana-934	24	37	functions	function	NOUN
cana-934	24	38	exhibit	exhibit	VERB
cana-934	24	39	enhanced	enhance	VERB
cana-934	24	40	stability	stability	NOUN
cana-934	24	41	or	or	CCONJ
cana-934	24	42	propensity	propensity	NOUN
cana-934	24	43	for	for	ADP
cana-934	24	44	decay	decay	NOUN
cana-934	24	45	.	.	PUNCT
cana-934	25	1	2	2	X
cana-934	25	2	.	.	X
cana-934	25	3	analyze	analyze	NOUN
cana-934	25	4	decay	decay	VERB
cana-934	25	5	dynamic	dynamic	ADJ
cana-934	25	6	:	:	PUNCT
cana-934	25	7	explore	explore	VERB
cana-934	25	8	the	the	DET
cana-934	25	9	decay	decay	NOUN
cana-934	25	10	properties	property	NOUN
cana-934	25	11	of	of	ADP
cana-934	25	12	solutions	solution	NOUN
cana-934	25	13	in	in	ADP
cana-934	25	14	the	the	DET
cana-934	25	15	presence	presence	NOUN
cana-934	25	16	of	of	ADP
cana-934	25	17	time	time	NOUN
cana-934	25	18	-	-	PUNCT
cana-934	25	19	varying	vary	VERB
cana-934	25	20	coefficients	coefficient	NOUN
cana-934	25	21	,	,	PUNCT
cana-934	25	22	providing	provide	VERB
cana-934	25	23	a	a	DET
cana-934	25	24	deeper	deep	ADJ
cana-934	25	25	understanding	understanding	NOUN
cana-934	25	26	of	of	ADP
cana-934	25	27	how	how	SCONJ
cana-934	25	28	temporal	temporal	ADJ
cana-934	25	29	variations	variation	NOUN
cana-934	25	30	impact	impact	VERB
cana-934	25	31	the	the	DET
cana-934	25	32	longevity	longevity	NOUN
cana-934	25	33	and	and	CCONJ
cana-934	25	34	dissipation	dissipation	NOUN
cana-934	25	35	of	of	ADP
cana-934	25	36	wave	wave	NOUN
cana-934	25	37	packets	packet	NOUN
cana-934	25	38	.	.	PUNCT
cana-934	26	1	3	3	X
cana-934	26	2	.	.	X
cana-934	26	3	broaden	broaden	VERB
cana-934	26	4	applicability	applicability	NOUN
cana-934	26	5	:	:	PUNCT
cana-934	26	6	by	by	ADP
cana-934	26	7	extending	extend	VERB
cana-934	26	8	the	the	DET
cana-934	26	9	nlse	nlse	NOUN
cana-934	26	10	to	to	PART
cana-934	26	11	include	include	VERB
cana-934	26	12	time	time	NOUN
cana-934	26	13	-	-	PUNCT
cana-934	26	14	dependent	dependent	ADJ
cana-934	26	15	coefficients	coefficient	NOUN
cana-934	26	16	,	,	PUNCT
cana-934	26	17	our	our	PRON
cana-934	26	18	goal	goal	NOUN
cana-934	26	19	is	be	AUX
cana-934	26	20	to	to	PART
cana-934	26	21	widen	widen	VERB
cana-934	26	22	its	its	PRON
cana-934	26	23	applicability	applicability	NOUN
cana-934	26	24	to	to	ADP
cana-934	26	25	real	real	ADJ
cana-934	26	26	-	-	PUNCT
cana-934	26	27	world	world	NOUN
cana-934	26	28	systems	system	NOUN
cana-934	26	29	experiencing	experience	VERB
cana-934	26	30	temporal	temporal	ADJ
cana-934	26	31	changes	change	NOUN
cana-934	26	32	,	,	PUNCT
cana-934	26	33	offering	offer	VERB
cana-934	26	34	insights	insight	NOUN
cana-934	26	35	into	into	ADP
cana-934	26	36	their	their	PRON
cana-934	26	37	dynamics	dynamic	NOUN
cana-934	26	38	and	and	CCONJ
cana-934	26	39	facilitating	facilitate	VERB
cana-934	26	40	the	the	DET
cana-934	26	41	development	development	NOUN
cana-934	26	42	of	of	ADP
cana-934	26	43	more	more	ADV
cana-934	26	44	accurate	accurate	ADJ
cana-934	26	45	models	model	NOUN
cana-934	26	46	.	.	PUNCT
cana-934	27	1	through	through	ADP
cana-934	27	2	rigorous	rigorous	ADJ
cana-934	27	3	analytical	analytical	ADJ
cana-934	27	4	and	and	CCONJ
cana-934	27	5	numerical	numerical	ADJ
cana-934	27	6	analysis	analysis	NOUN
cana-934	27	7	,	,	PUNCT
cana-934	27	8	this	this	DET
cana-934	27	9	research	research	NOUN
cana-934	27	10	endeavors	endeavor	VERB
cana-934	27	11	to	to	PART
cana-934	27	12	illuminate	illuminate	VERB
cana-934	27	13	the	the	DET
cana-934	27	14	dynamic	dynamic	ADJ
cana-934	27	15	interplay	interplay	NOUN
cana-934	27	16	between	between	ADP
cana-934	27	17	nonlinearity	nonlinearity	NOUN
cana-934	27	18	,	,	PUNCT
cana-934	27	19	dispersion	dispersion	NOUN
cana-934	27	20	,	,	PUNCT
cana-934	27	21	and	and	CCONJ
cana-934	27	22	temporal	temporal	ADJ
cana-934	27	23	variation	variation	NOUN
cana-934	27	24	,	,	PUNCT
cana-934	27	25	contributing	contribute	VERB
cana-934	27	26	valuable	valuable	ADJ
cana-934	27	27	knowledge	knowledge	NOUN
cana-934	27	28	to	to	ADP
cana-934	27	29	the	the	DET
cana-934	27	30	fields	field	NOUN
cana-934	27	31	governed	govern	VERB
cana-934	27	32	by	by	ADP
cana-934	27	33	the	the	DET
cana-934	27	34	nlse	nlse	NOUN
cana-934	27	35	and	and	CCONJ
cana-934	27	36	paving	pave	VERB
cana-934	27	37	the	the	DET
cana-934	27	38	way	way	NOUN
cana-934	27	39	for	for	ADP
cana-934	27	40	innovations	innovation	NOUN
cana-934	27	41	in	in	ADP
cana-934	27	42	modeling	model	VERB
cana-934	27	43	complex	complex	ADJ
cana-934	27	44	systems	system	NOUN
cana-934	27	45	.	.	PUNCT
cana-934	28	1	2	2	X
cana-934	28	2	.	.	X
cana-934	28	3	theoretical	theoretical	ADJ
cana-934	28	4	framework	framework	NOUN
cana-934	28	5	quantum	quantum	NOUN
cana-934	28	6	noise	noise	NOUN
cana-934	28	7	-	-	PUNCT
cana-934	28	8	extended	extend	VERB
cana-934	28	9	nlse	nlse	NOUN
cana-934	28	10	(	(	PUNCT
cana-934	28	11	qnlse	qnlse	PROPN
cana-934	28	12	)	)	PUNCT
cana-934	28	13	the	the	DET
cana-934	28	14	quantum	quantum	NOUN
cana-934	28	15	noise	noise	NOUN
cana-934	28	16	-	-	PUNCT
cana-934	28	17	extended	extend	VERB
cana-934	28	18	nonlinear	nonlinear	ADJ
cana-934	28	19	schrödinger	schrödinger	ADJ
cana-934	28	20	equation	equation	NOUN
cana-934	28	21	(	(	PUNCT
cana-934	28	22	qnlse	qnlse	ADJ
cana-934	28	23	)	)	PUNCT
cana-934	28	24	enhances	enhance	VERB
cana-934	28	25	the	the	DET
cana-934	28	26	classical	classical	ADJ
cana-934	28	27	nlse	nlse	NOUN
cana-934	28	28	by	by	ADP
cana-934	28	29	incorporating	incorporate	VERB
cana-934	28	30	quantum	quantum	ADJ
cana-934	28	31	fluctuations	fluctuation	NOUN
cana-934	28	32	and	and	CCONJ
cana-934	28	33	noise	noise	NOUN
cana-934	28	34	,	,	PUNCT
cana-934	28	35	reflecting	reflect	VERB
cana-934	28	36	the	the	DET
cana-934	28	37	stochastic	stochastic	ADJ
cana-934	28	38	nature	nature	NOUN
cana-934	28	39	of	of	ADP
cana-934	28	40	quantum	quantum	NOUN
cana-934	28	41	systems	system	NOUN
cana-934	28	42	.	.	PUNCT
cana-934	29	1	this	this	DET
cana-934	29	2	extension	extension	NOUN
cana-934	29	3	is	be	AUX
cana-934	29	4	pivotal	pivotal	ADJ
cana-934	29	5	for	for	ADP
cana-934	29	6	modeling	model	VERB
cana-934	29	7	the	the	DET
cana-934	29	8	behavior	behavior	NOUN
cana-934	29	9	of	of	ADP
cana-934	29	10	quantum	quantum	NOUN
cana-934	29	11	systems	system	NOUN
cana-934	29	12	more	more	ADV
cana-934	29	13	accurately	accurately	ADV
cana-934	29	14	,	,	PUNCT
cana-934	29	15	particularly	particularly	ADV
cana-934	29	16	in	in	ADP
cana-934	29	17	environments	environment	NOUN
cana-934	29	18	where	where	SCONJ
cana-934	29	19	quantum	quantum	NOUN
cana-934	29	20	noise	noise	NOUN
cana-934	29	21	plays	play	VERB
cana-934	29	22	a	a	DET
cana-934	29	23	significant	significant	ADJ
cana-934	29	24	role	role	NOUN
cana-934	29	25	,	,	PUNCT
cana-934	29	26	such	such	ADJ
cana-934	29	27	as	as	ADP
cana-934	29	28	in	in	ADP
cana-934	29	29	optical	optical	ADJ
cana-934	29	30	fibers	fiber	NOUN
cana-934	29	31	at	at	ADP
cana-934	29	32	the	the	DET
cana-934	29	33	quantum	quantum	ADJ
cana-934	29	34	limit	limit	NOUN
cana-934	29	35	and	and	CCONJ
cana-934	29	36	bose	bose	NOUN
cana-934	29	37	-	-	PUNCT
cana-934	29	38	einstein	einstein	NOUN
cana-934	29	39	condensates	condensate	NOUN
cana-934	29	40	.	.	PUNCT
cana-934	30	1	mathematical	mathematical	ADJ
cana-934	30	2	formulation	formulation	NOUN
cana-934	30	3	:	:	PUNCT
cana-934	30	4	the	the	DET
cana-934	30	5	qnlse	qnlse	NOUN
cana-934	30	6	can	can	AUX
cana-934	30	7	be	be	AUX
cana-934	30	8	represented	represent	VERB
cana-934	30	9	as	as	ADP
cana-934	30	10	:	:	PUNCT
cana-934	30	11	𝑖ℏ	𝑖ℏ	PART
cana-934	30	12	𝜕𝜓	𝜕𝜓	NOUN
cana-934	30	13	𝜕𝑡	𝜕𝑡	NOUN
cana-934	31	1	=	=	X
cana-934	31	2	(	(	PUNCT
cana-934	31	3	−	−	NOUN
cana-934	31	4	ℏ2	ℏ2	NOUN
cana-934	31	5	2𝑚	2𝑚	VERB
cana-934	31	6	𝛻2	𝛻2	NOUN
cana-934	31	7	+	+	PUNCT
cana-934	31	8	𝑉(𝒓	𝑉(𝒓	PROPN
cana-934	31	9	,	,	PUNCT
cana-934	31	10	𝑡	𝑡	NOUN
cana-934	31	11	)	)	PUNCT
cana-934	31	12	+	+	CCONJ
cana-934	31	13	𝑔	𝑔	PROPN
cana-934	31	14	∣	∣	ADJ
cana-934	31	15	∣	∣	ADJ
cana-934	31	16	∣	∣	ADJ
cana-934	31	17	𝜓	𝜓	PROPN
cana-934	31	18	∣	∣	ADJ
cana-934	31	19	∣	∣	ADJ
cana-934	31	20	∣	∣	ADJ
cana-934	31	21	2	2	NUM
cana-934	31	22	)	)	PUNCT
cana-934	31	23	𝜓	𝜓	NOUN
cana-934	32	1	+	+	PROPN
cana-934	32	2	𝑖𝛩(𝒓	𝑖𝛩(𝒓	PROPN
cana-934	32	3	,	,	PUNCT
cana-934	32	4	𝑡)𝜓	𝑡)𝜓	PUNCT
cana-934	32	5	+	+	CCONJ
cana-934	32	6	𝛯(𝒓	𝛯(𝒓	NUM
cana-934	32	7	,	,	PUNCT
cana-934	32	8	𝑡	𝑡	NOUN
cana-934	32	9	)	)	PUNCT
cana-934	32	10	,	,	PUNCT
cana-934	32	11	where	where	SCONJ
cana-934	32	12	:	:	PUNCT
cana-934	32	13	•	•	ADP
cana-934	32	14	ψ(r	ψ(r	PROPN
cana-934	32	15	,	,	PUNCT
cana-934	32	16	t	t	PROPN
cana-934	32	17	)	)	PUNCT
cana-934	32	18	is	be	AUX
cana-934	32	19	the	the	DET
cana-934	32	20	wave	wave	NOUN
cana-934	32	21	function	function	NOUN
cana-934	32	22	,	,	PUNCT
cana-934	32	23	•	•	NUM
cana-934	32	24	ℏ	ℏ	PROPN
cana-934	32	25	is	be	AUX
cana-934	32	26	the	the	DET
cana-934	32	27	reduced	reduce	VERB
cana-934	32	28	planck	planck	NOUN
cana-934	32	29	's	's	PART
cana-934	32	30	constant	constant	ADJ
cana-934	32	31	,	,	PUNCT
cana-934	32	32	•	•	NUM
cana-934	32	33	m	m	NOUN
cana-934	32	34	is	be	AUX
cana-934	32	35	the	the	DET
cana-934	32	36	mass	mass	NOUN
cana-934	32	37	of	of	ADP
cana-934	32	38	the	the	DET
cana-934	32	39	particle	particle	NOUN
cana-934	32	40	,	,	PUNCT
cana-934	32	41	•	•	PROPN
cana-934	32	42	v(r	v(r	PROPN
cana-934	32	43	,	,	PUNCT
cana-934	32	44	t	t	PROPN
cana-934	32	45	)	)	PUNCT
cana-934	32	46	represents	represent	VERB
cana-934	32	47	the	the	DET
cana-934	32	48	external	external	ADJ
cana-934	32	49	potential	potential	NOUN
cana-934	32	50	,	,	PUNCT
cana-934	32	51	which	which	PRON
cana-934	32	52	can	can	AUX
cana-934	32	53	be	be	AUX
cana-934	32	54	time	time	NOUN
cana-934	32	55	-	-	PUNCT
cana-934	32	56	dependent	dependent	ADJ
cana-934	32	57	,	,	PUNCT
cana-934	32	58	•	•	NUM
cana-934	32	59	g	g	PROPN
cana-934	32	60	denotes	denote	VERB
cana-934	32	61	the	the	DET
cana-934	32	62	nonlinear	nonlinear	ADJ
cana-934	32	63	interaction	interaction	NOUN
cana-934	32	64	strength	strength	NOUN
cana-934	32	65	,	,	PUNCT
cana-934	32	66	communications	communication	NOUN
cana-934	32	67	on	on	ADP
cana-934	32	68	applied	apply	VERB
cana-934	32	69	nonlinear	nonlinear	ADJ
cana-934	32	70	analysis	analysis	NOUN
cana-934	32	71	issn	issn	NOUN
cana-934	32	72	:	:	PUNCT
cana-934	32	73	1074	1074	NUM
cana-934	32	74	-	-	PUNCT
cana-934	32	75	133x	133x	NUM
cana-934	32	76	vol	vol	NOUN
cana-934	32	77	31	31	NUM
cana-934	32	78	no	no	NOUN
cana-934	32	79	.	.	PUNCT
cana-934	33	1	4s	4s	NUM
cana-934	33	2	(	(	PUNCT
cana-934	33	3	2024	2024	NUM
cana-934	33	4	)	)	PUNCT
cana-934	33	5	412	412	NUM
cana-934	33	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-934	33	7	•	•	ADP
cana-934	33	8	θ(r	θ(r	PROPN
cana-934	33	9	,	,	PUNCT
cana-934	33	10	t	t	PROPN
cana-934	33	11	)	)	PUNCT
cana-934	33	12	corresponds	correspond	VERB
cana-934	33	13	to	to	ADP
cana-934	33	14	dissipative	dissipative	NOUN
cana-934	33	15	processes	process	NOUN
cana-934	33	16	,	,	PUNCT
cana-934	33	17	•	•	ADP
cana-934	33	18	ξ(r	ξ(r	PROPN
cana-934	33	19	,	,	PUNCT
cana-934	33	20	t	t	PROPN
cana-934	33	21	)	)	PUNCT
cana-934	33	22	represents	represent	VERB
cana-934	33	23	the	the	DET
cana-934	33	24	quantum	quantum	ADJ
cana-934	33	25	noise	noise	NOUN
cana-934	33	26	term	term	NOUN
cana-934	33	27	,	,	PUNCT
cana-934	33	28	capturing	capture	VERB
cana-934	33	29	the	the	DET
cana-934	33	30	inherent	inherent	ADJ
cana-934	33	31	fluctuations	fluctuation	NOUN
cana-934	33	32	in	in	ADP
cana-934	33	33	the	the	DET
cana-934	33	34	system	system	NOUN
cana-934	33	35	.	.	PUNCT
cana-934	34	1	significance	significance	NOUN
cana-934	34	2	of	of	ADP
cana-934	34	3	terms	term	NOUN
cana-934	34	4	:	:	PUNCT
cana-934	34	5	•	•	ADP
cana-934	34	6	the	the	DET
cana-934	34	7	laplacian	laplacian	ADJ
cana-934	34	8	𝛻2𝜓	𝛻2𝜓	NOUN
cana-934	34	9	term	term	NOUN
cana-934	34	10	accounts	account	NOUN
cana-934	34	11	for	for	ADP
cana-934	34	12	the	the	DET
cana-934	34	13	spread	spread	NOUN
cana-934	34	14	of	of	ADP
cana-934	34	15	the	the	DET
cana-934	34	16	wave	wave	NOUN
cana-934	34	17	packet	packet	NOUN
cana-934	34	18	,	,	PUNCT
cana-934	34	19	while	while	SCONJ
cana-934	34	20	the	the	DET
cana-934	34	21	potential	potential	ADJ
cana-934	34	22	v(r	v(r	PROPN
cana-934	34	23	,	,	PUNCT
cana-934	34	24	t	t	PROPN
cana-934	34	25	)	)	PUNCT
cana-934	34	26	influences	influence	VERB
cana-934	34	27	its	its	PRON
cana-934	34	28	motion	motion	NOUN
cana-934	34	29	through	through	ADP
cana-934	34	30	external	external	ADJ
cana-934	34	31	forces	force	NOUN
cana-934	34	32	.	.	PUNCT
cana-934	35	1	•	•	NUM
cana-934	35	2	nonlinear	nonlinear	ADJ
cana-934	35	3	interaction	interaction	NOUN
cana-934	35	4	term	term	NOUN
cana-934	35	5	𝑔	𝑔	PROPN
cana-934	35	6	∣	∣	PROPN
cana-934	35	7	𝜓	𝜓	PROPN
cana-934	35	8	∣2	∣2	PRON
cana-934	35	9	𝜓	𝜓	PROPN
cana-934	35	10	captures	capture	VERB
cana-934	35	11	the	the	DET
cana-934	35	12	self	self	NOUN
cana-934	35	13	-	-	PUNCT
cana-934	35	14	interaction	interaction	NOUN
cana-934	35	15	among	among	ADP
cana-934	35	16	particles	particle	NOUN
cana-934	35	17	,	,	PUNCT
cana-934	35	18	a	a	DET
cana-934	35	19	crucial	crucial	ADJ
cana-934	35	20	aspect	aspect	NOUN
cana-934	35	21	of	of	ADP
cana-934	35	22	many	many	ADJ
cana-934	35	23	-	-	PUNCT
cana-934	35	24	body	body	NOUN
cana-934	35	25	quantum	quantum	NOUN
cana-934	35	26	systems	system	NOUN
cana-934	35	27	.	.	PUNCT
cana-934	36	1	•	•	NUM
cana-934	36	2	dissipative	dissipative	ADJ
cana-934	36	3	term	term	NOUN
cana-934	36	4	θ(r	θ(r	NOUN
cana-934	36	5	,	,	PUNCT
cana-934	36	6	t)ψ	t)ψ	NOUN
cana-934	36	7	models	model	VERB
cana-934	36	8	energy	energy	NOUN
cana-934	36	9	loss	loss	NOUN
cana-934	36	10	or	or	CCONJ
cana-934	36	11	gain	gain	NOUN
cana-934	36	12	,	,	PUNCT
cana-934	36	13	vital	vital	ADJ
cana-934	36	14	for	for	ADP
cana-934	36	15	open	open	ADJ
cana-934	36	16	quantum	quantum	NOUN
cana-934	36	17	systems	system	NOUN
cana-934	36	18	.	.	PUNCT
cana-934	37	1	•	•	NUM
cana-934	37	2	quantum	quantum	NOUN
cana-934	37	3	noise	noise	NOUN
cana-934	37	4	term	term	NOUN
cana-934	37	5	ξ(r	ξ(r	PROPN
cana-934	37	6	,	,	PUNCT
cana-934	37	7	t	t	PROPN
cana-934	37	8	)	)	PUNCT
cana-934	37	9	introduces	introduce	VERB
cana-934	37	10	stochasticity	stochasticity	NOUN
cana-934	37	11	,	,	PUNCT
cana-934	37	12	acknowledging	acknowledge	VERB
cana-934	37	13	the	the	DET
cana-934	37	14	unpredictable	unpredictable	ADJ
cana-934	37	15	quantum	quantum	ADJ
cana-934	37	16	fluctuations	fluctuation	NOUN
cana-934	37	17	.	.	PUNCT
cana-934	38	1	multi	multi	ADJ
cana-934	38	2	-	-	ADJ
cana-934	38	3	particle	particle	ADJ
cana-934	38	4	dynamics	dynamic	NOUN
cana-934	38	5	the	the	DET
cana-934	38	6	extension	extension	NOUN
cana-934	38	7	to	to	ADP
cana-934	38	8	multi	multi	ADJ
cana-934	38	9	-	-	ADJ
cana-934	38	10	particle	particle	ADJ
cana-934	38	11	systems	system	NOUN
cana-934	38	12	necessitates	necessitate	VERB
cana-934	38	13	the	the	DET
cana-934	38	14	inclusion	inclusion	NOUN
cana-934	38	15	of	of	ADP
cana-934	38	16	interaction	interaction	NOUN
cana-934	38	17	terms	term	NOUN
cana-934	38	18	among	among	ADP
cana-934	38	19	particles	particle	NOUN
cana-934	38	20	,	,	PUNCT
cana-934	38	21	critical	critical	ADJ
cana-934	38	22	for	for	ADP
cana-934	38	23	accurately	accurately	ADV
cana-934	38	24	depicting	depict	VERB
cana-934	38	25	phenomena	phenomenon	NOUN
cana-934	38	26	like	like	ADP
cana-934	38	27	entanglement	entanglement	NOUN
cana-934	38	28	and	and	CCONJ
cana-934	38	29	collective	collective	ADJ
cana-934	38	30	behaviors	behavior	NOUN
cana-934	38	31	.	.	PUNCT
cana-934	39	1	equations	equation	NOUN
cana-934	39	2	modeling	model	VERB
cana-934	39	3	multi	multi	ADJ
cana-934	39	4	-	-	ADJ
cana-934	39	5	particle	particle	ADJ
cana-934	39	6	interactions	interaction	NOUN
cana-934	39	7	:	:	PUNCT
cana-934	39	8	for	for	ADP
cana-934	39	9	a	a	DET
cana-934	39	10	system	system	NOUN
cana-934	39	11	of	of	ADP
cana-934	39	12	n	n	DET
cana-934	39	13	interacting	interact	VERB
cana-934	39	14	particles	particle	NOUN
cana-934	39	15	,	,	PUNCT
cana-934	39	16	the	the	DET
cana-934	39	17	qnlse	qnlse	NOUN
cana-934	39	18	modifies	modify	VERB
cana-934	39	19	to	to	PART
cana-934	39	20	accommodate	accommodate	VERB
cana-934	39	21	the	the	DET
cana-934	39	22	sum	sum	NOUN
cana-934	39	23	of	of	ADP
cana-934	39	24	all	all	DET
cana-934	39	25	pairwise	pairwise	NOUN
cana-934	39	26	interactions	interaction	NOUN
cana-934	39	27	:	:	PUNCT
cana-934	39	28	𝑖ℏ	𝑖ℏ	X
cana-934	39	29	𝜕𝜓𝑖	𝜕𝜓𝑖	PUNCT
cana-934	40	1	𝜕𝑡	𝜕𝑡	NOUN
cana-934	40	2	=	=	SYM
cana-934	41	1	[	[	X
cana-934	41	2	−	−	NOUN
cana-934	41	3	ℏ2	ℏ2	NOUN
cana-934	41	4	2𝑚𝑖	2𝑚𝑖	VERB
cana-934	41	5	𝛻2	𝛻2	NOUN
cana-934	41	6	+	+	CCONJ
cana-934	41	7	𝑉𝑖(𝒓𝑖	𝑉𝑖(𝒓𝑖	NOUN
cana-934	41	8	,	,	PUNCT
cana-934	41	9	𝑡	𝑡	X
cana-934	41	10	)	)	PUNCT
cana-934	41	11	+	+	CCONJ
cana-934	41	12	∑	∑	PUNCT
cana-934	41	13	𝑈𝑖𝑗	𝑈𝑖𝑗	PROPN
cana-934	41	14	∣	∣	NOUN
cana-934	41	15	𝜓𝑗	𝜓𝑗	VERB
cana-934	41	16	∣2]𝜓𝑖	∣2]𝜓𝑖	PROPN
cana-934	41	17	+	+	CCONJ
cana-934	41	18	𝑗≠𝑖	𝑗≠𝑖	X
cana-934	41	19	noise	noise	NOUN
cana-934	41	20	and	and	CCONJ
cana-934	41	21	dissipation	dissipation	NOUN
cana-934	41	22	terms	term	NOUN
cana-934	41	23	,	,	PUNCT
cana-934	41	24	where	where	SCONJ
cana-934	41	25	:	:	PUNCT
cana-934	41	26	•	•	NOUN
cana-934	41	27	uij	uij	PRON
cana-934	41	28	represents	represent	VERB
cana-934	41	29	the	the	DET
cana-934	41	30	interaction	interaction	NOUN
cana-934	41	31	strength	strength	NOUN
cana-934	41	32	between	between	ADP
cana-934	41	33	particles	particle	NOUN
cana-934	41	34	i	i	PRON
cana-934	41	35	and	and	CCONJ
cana-934	41	36	j	j	PROPN
cana-934	41	37	,	,	PUNCT
cana-934	42	1	•	•	NUM
cana-934	42	2	vi(ri	vi(ri	PROPN
cana-934	42	3	,	,	PUNCT
cana-934	42	4	t	t	PROPN
cana-934	42	5	)	)	PUNCT
cana-934	42	6	is	be	AUX
cana-934	42	7	the	the	DET
cana-934	42	8	external	external	ADJ
cana-934	42	9	potential	potential	NOUN
cana-934	42	10	affecting	affect	VERB
cana-934	42	11	the	the	DET
cana-934	42	12	i	i	PROPN
cana-934	42	13	th	th	X
cana-934	42	14	particle	particle	NOUN
cana-934	42	15	.	.	PUNCT
cana-934	43	1	importance	importance	NOUN
cana-934	43	2	of	of	ADP
cana-934	43	3	multi	multi	ADJ
cana-934	43	4	-	-	ADJ
cana-934	43	5	particle	particle	ADJ
cana-934	43	6	dynamics	dynamic	NOUN
cana-934	43	7	:	:	PUNCT
cana-934	43	8	•	•	NUM
cana-934	43	9	capturing	capture	VERB
cana-934	43	10	the	the	DET
cana-934	43	11	essence	essence	NOUN
cana-934	43	12	of	of	ADP
cana-934	43	13	quantum	quantum	NOUN
cana-934	43	14	correlations	correlation	NOUN
cana-934	43	15	and	and	CCONJ
cana-934	43	16	entanglement	entanglement	NOUN
cana-934	43	17	,	,	PUNCT
cana-934	43	18	essential	essential	ADJ
cana-934	43	19	for	for	ADP
cana-934	43	20	quantum	quantum	NOUN
cana-934	43	21	information	information	NOUN
cana-934	43	22	processing	processing	NOUN
cana-934	43	23	.	.	PUNCT
cana-934	44	1	•	•	NUM
cana-934	44	2	allowing	allow	VERB
cana-934	44	3	the	the	DET
cana-934	44	4	study	study	NOUN
cana-934	44	5	of	of	ADP
cana-934	44	6	collective	collective	ADJ
cana-934	44	7	excitations	excitation	NOUN
cana-934	44	8	and	and	CCONJ
cana-934	44	9	the	the	DET
cana-934	44	10	emergence	emergence	NOUN
cana-934	44	11	of	of	ADP
cana-934	44	12	complex	complex	ADJ
cana-934	44	13	phenomena	phenomenon	NOUN
cana-934	44	14	such	such	ADJ
cana-934	44	15	as	as	ADP
cana-934	44	16	superfluidity	superfluidity	NOUN
cana-934	44	17	and	and	CCONJ
cana-934	44	18	quantum	quantum	NOUN
cana-934	44	19	phase	phase	NOUN
cana-934	44	20	transitions	transition	NOUN
cana-934	44	21	.	.	PUNCT
cana-934	45	1	3	3	X
cana-934	45	2	.	.	X
cana-934	45	3	methodology	methodology	NOUN
cana-934	45	4	this	this	DET
cana-934	45	5	section	section	NOUN
cana-934	45	6	delineates	delineate	VERB
cana-934	45	7	the	the	DET
cana-934	45	8	comprehensive	comprehensive	ADJ
cana-934	45	9	methodology	methodology	NOUN
cana-934	45	10	employed	employ	VERB
cana-934	45	11	to	to	PART
cana-934	45	12	scrutinize	scrutinize	VERB
cana-934	45	13	the	the	DET
cana-934	45	14	quantum	quantum	NOUN
cana-934	45	15	noiseextended	noiseextende	VERB
cana-934	45	16	nonlinear	nonlinear	ADJ
cana-934	45	17	schrödinger	schrödinger	ADJ
cana-934	45	18	equation	equation	NOUN
cana-934	45	19	(	(	PUNCT
cana-934	45	20	qnlse	qnlse	PROPN
cana-934	45	21	)	)	PUNCT
cana-934	45	22	,	,	PUNCT
cana-934	45	23	incorporating	incorporate	VERB
cana-934	45	24	both	both	PRON
cana-934	45	25	analytical	analytical	ADJ
cana-934	45	26	techniques	technique	NOUN
cana-934	45	27	and	and	CCONJ
cana-934	45	28	numerical	numerical	ADJ
cana-934	45	29	simulations	simulation	NOUN
cana-934	45	30	to	to	PART
cana-934	45	31	unveil	unveil	VERB
cana-934	45	32	the	the	DET
cana-934	45	33	stability	stability	NOUN
cana-934	45	34	,	,	PUNCT
cana-934	45	35	decay	decay	NOUN
cana-934	45	36	properties	property	NOUN
cana-934	45	37	,	,	PUNCT
cana-934	45	38	and	and	CCONJ
cana-934	45	39	multi	multi	ADJ
cana-934	45	40	-	-	ADJ
cana-934	45	41	particle	particle	ADJ
cana-934	45	42	dynamics	dynamic	NOUN
cana-934	45	43	governed	govern	VERB
cana-934	45	44	by	by	ADP
cana-934	45	45	the	the	DET
cana-934	45	46	equation	equation	NOUN
cana-934	45	47	.	.	PUNCT
cana-934	46	1	communications	communication	NOUN
cana-934	46	2	on	on	ADP
cana-934	46	3	applied	apply	VERB
cana-934	46	4	nonlinear	nonlinear	ADJ
cana-934	46	5	analysis	analysis	NOUN
cana-934	46	6	issn	issn	NOUN
cana-934	46	7	:	:	PUNCT
cana-934	46	8	1074	1074	NUM
cana-934	46	9	-	-	PUNCT
cana-934	46	10	133x	133x	NUM
cana-934	46	11	vol	vol	NOUN
cana-934	46	12	31	31	NUM
cana-934	46	13	no	no	NOUN
cana-934	46	14	.	.	PUNCT
cana-934	47	1	4s	4s	NUM
cana-934	47	2	(	(	PUNCT
cana-934	47	3	2024	2024	NUM
cana-934	47	4	)	)	PUNCT
cana-934	47	5	413	413	NUM
cana-934	47	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-934	47	7	analytical	analytical	ADJ
cana-934	47	8	methods	method	NOUN
cana-934	47	9	our	our	PRON
cana-934	47	10	analytical	analytical	ADJ
cana-934	47	11	approach	approach	NOUN
cana-934	47	12	to	to	ADP
cana-934	47	13	understanding	understand	VERB
cana-934	47	14	the	the	DET
cana-934	47	15	qnlse	qnlse	NOUN
cana-934	47	16	focuses	focus	VERB
cana-934	47	17	on	on	ADP
cana-934	47	18	leveraging	leverage	VERB
cana-934	47	19	perturbation	perturbation	NOUN
cana-934	47	20	theory	theory	NOUN
cana-934	47	21	and	and	CCONJ
cana-934	47	22	spectral	spectral	ADJ
cana-934	47	23	analysis	analysis	NOUN
cana-934	47	24	,	,	PUNCT
cana-934	47	25	which	which	PRON
cana-934	47	26	are	be	AUX
cana-934	47	27	instrumental	instrumental	ADJ
cana-934	47	28	in	in	ADP
cana-934	47	29	dissecting	dissect	VERB
cana-934	47	30	the	the	DET
cana-934	47	31	equation	equation	NOUN
cana-934	47	32	's	's	PART
cana-934	47	33	complex	complex	ADJ
cana-934	47	34	behaviors	behavior	NOUN
cana-934	47	35	under	under	ADP
cana-934	47	36	various	various	ADJ
cana-934	47	37	conditions	condition	NOUN
cana-934	47	38	.	.	PUNCT
cana-934	48	1	perturbation	perturbation	NOUN
cana-934	48	2	theory	theory	NOUN
cana-934	48	3	:	:	PUNCT
cana-934	48	4	this	this	DET
cana-934	48	5	method	method	NOUN
cana-934	48	6	is	be	AUX
cana-934	48	7	pivotal	pivotal	ADJ
cana-934	48	8	for	for	ADP
cana-934	48	9	examining	examine	VERB
cana-934	48	10	the	the	DET
cana-934	48	11	stability	stability	NOUN
cana-934	48	12	of	of	ADP
cana-934	48	13	solutions	solution	NOUN
cana-934	48	14	to	to	ADP
cana-934	48	15	the	the	DET
cana-934	48	16	qnlse	qnlse	NOUN
cana-934	48	17	,	,	PUNCT
cana-934	48	18	especially	especially	ADV
cana-934	48	19	in	in	ADP
cana-934	48	20	scenarios	scenario	NOUN
cana-934	48	21	where	where	SCONJ
cana-934	48	22	the	the	DET
cana-934	48	23	quantum	quantum	NOUN
cana-934	48	24	noise	noise	NOUN
cana-934	48	25	and	and	CCONJ
cana-934	48	26	interaction	interaction	NOUN
cana-934	48	27	terms	term	NOUN
cana-934	48	28	are	be	AUX
cana-934	48	29	treated	treat	VERB
cana-934	48	30	as	as	ADP
cana-934	48	31	small	small	ADJ
cana-934	48	32	perturbations	perturbation	NOUN
cana-934	48	33	to	to	ADP
cana-934	48	34	the	the	DET
cana-934	48	35	classical	classical	ADJ
cana-934	48	36	nlse	nlse	NOUN
cana-934	48	37	.	.	PUNCT
cana-934	49	1	by	by	ADP
cana-934	49	2	introducing	introduce	VERB
cana-934	49	3	a	a	DET
cana-934	49	4	small	small	ADJ
cana-934	49	5	parameter	parameter	NOUN
cana-934	49	6	,	,	PUNCT
cana-934	49	7	ϵ	ϵ	X
cana-934	49	8	,	,	PUNCT
cana-934	49	9	to	to	PART
cana-934	49	10	scale	scale	VERB
cana-934	49	11	the	the	DET
cana-934	49	12	perturbations	perturbation	NOUN
cana-934	49	13	,	,	PUNCT
cana-934	49	14	we	we	PRON
cana-934	49	15	expand	expand	VERB
cana-934	49	16	the	the	DET
cana-934	49	17	wave	wave	NOUN
cana-934	49	18	function	function	NOUN
cana-934	49	19	in	in	ADP
cana-934	49	20	powers	power	NOUN
cana-934	49	21	of	of	ADP
cana-934	49	22	ϵ	ϵ	PROPN
cana-934	49	23	and	and	CCONJ
cana-934	49	24	systematically	systematically	ADV
cana-934	49	25	analyze	analyze	VERB
cana-934	49	26	the	the	DET
cana-934	49	27	resulting	result	VERB
cana-934	49	28	hierarchy	hierarchy	NOUN
cana-934	49	29	of	of	ADP
cana-934	49	30	equations	equation	NOUN
cana-934	49	31	.	.	PUNCT
cana-934	50	1	this	this	DET
cana-934	50	2	approach	approach	NOUN
cana-934	50	3	elucidates	elucidate	VERB
cana-934	50	4	the	the	DET
cana-934	50	5	conditions	condition	NOUN
cana-934	50	6	under	under	ADP
cana-934	50	7	which	which	PRON
cana-934	50	8	perturbations	perturbation	NOUN
cana-934	50	9	grow	grow	VERB
cana-934	50	10	or	or	CCONJ
cana-934	50	11	decay	decay	VERB
cana-934	50	12	,	,	PUNCT
cana-934	50	13	thereby	thereby	ADV
cana-934	50	14	determining	determine	VERB
cana-934	50	15	the	the	DET
cana-934	50	16	stability	stability	NOUN
cana-934	50	17	of	of	ADP
cana-934	50	18	the	the	DET
cana-934	50	19	system	system	NOUN
cana-934	50	20	.	.	PUNCT
cana-934	51	1	spectral	spectral	ADJ
cana-934	51	2	analysis	analysis	NOUN
cana-934	51	3	:	:	PUNCT
cana-934	51	4	to	to	PART
cana-934	51	5	further	far	ADV
cana-934	51	6	understand	understand	VERB
cana-934	51	7	the	the	DET
cana-934	51	8	dynamics	dynamic	NOUN
cana-934	51	9	of	of	ADP
cana-934	51	10	the	the	DET
cana-934	51	11	qnlse	qnlse	NOUN
cana-934	51	12	,	,	PUNCT
cana-934	51	13	we	we	PRON
cana-934	51	14	employ	employ	VERB
cana-934	51	15	spectral	spectral	ADJ
cana-934	51	16	analysis	analysis	NOUN
cana-934	51	17	to	to	PART
cana-934	51	18	examine	examine	VERB
cana-934	51	19	the	the	DET
cana-934	51	20	dispersion	dispersion	NOUN
cana-934	51	21	relations	relation	NOUN
cana-934	51	22	and	and	CCONJ
cana-934	51	23	eigenvalue	eigenvalue	ADJ
cana-934	51	24	spectra	spectra	NOUN
cana-934	51	25	of	of	ADP
cana-934	51	26	linearized	linearize	VERB
cana-934	51	27	versions	version	NOUN
cana-934	51	28	of	of	ADP
cana-934	51	29	the	the	DET
cana-934	51	30	equation	equation	NOUN
cana-934	51	31	.	.	PUNCT
cana-934	52	1	this	this	DET
cana-934	52	2	technique	technique	NOUN
cana-934	52	3	sheds	shed	VERB
cana-934	52	4	light	light	NOUN
cana-934	52	5	on	on	ADP
cana-934	52	6	the	the	DET
cana-934	52	7	propagation	propagation	NOUN
cana-934	52	8	characteristics	characteristic	NOUN
cana-934	52	9	of	of	ADP
cana-934	52	10	wave	wave	NOUN
cana-934	52	11	packets	packet	NOUN
cana-934	52	12	and	and	CCONJ
cana-934	52	13	the	the	DET
cana-934	52	14	influence	influence	NOUN
cana-934	52	15	of	of	ADP
cana-934	52	16	timedependent	timedependent	NOUN
cana-934	52	17	coefficients	coefficient	NOUN
cana-934	52	18	and	and	CCONJ
cana-934	52	19	quantum	quantum	NOUN
cana-934	52	20	noise	noise	NOUN
cana-934	52	21	on	on	ADP
cana-934	52	22	the	the	DET
cana-934	52	23	system	system	NOUN
cana-934	52	24	's	's	PART
cana-934	52	25	spectral	spectral	ADJ
cana-934	52	26	properties	property	NOUN
cana-934	52	27	.	.	PUNCT
cana-934	53	1	numerical	numerical	ADJ
cana-934	53	2	simulations	simulation	NOUN
cana-934	53	3	given	give	VERB
cana-934	53	4	the	the	DET
cana-934	53	5	inherent	inherent	ADJ
cana-934	53	6	complexity	complexity	NOUN
cana-934	53	7	of	of	ADP
cana-934	53	8	the	the	DET
cana-934	53	9	qnlse	qnlse	NOUN
cana-934	53	10	,	,	PUNCT
cana-934	53	11	especially	especially	ADV
cana-934	53	12	with	with	ADP
cana-934	53	13	time	time	NOUN
cana-934	53	14	-	-	PUNCT
cana-934	53	15	dependent	dependent	ADJ
cana-934	53	16	coefficients	coefficient	NOUN
cana-934	53	17	and	and	CCONJ
cana-934	53	18	multiparticle	multiparticle	NOUN
cana-934	53	19	interactions	interaction	NOUN
cana-934	53	20	,	,	PUNCT
cana-934	53	21	numerical	numerical	ADJ
cana-934	53	22	simulations	simulation	NOUN
cana-934	53	23	play	play	VERB
cana-934	53	24	a	a	DET
cana-934	53	25	crucial	crucial	ADJ
cana-934	53	26	role	role	NOUN
cana-934	53	27	in	in	ADP
cana-934	53	28	our	our	PRON
cana-934	53	29	methodology	methodology	NOUN
cana-934	53	30	.	.	PUNCT
cana-934	54	1	we	we	PRON
cana-934	54	2	utilize	utilize	VERB
cana-934	54	3	a	a	DET
cana-934	54	4	combination	combination	NOUN
cana-934	54	5	of	of	ADP
cana-934	54	6	finite	finite	ADJ
cana-934	54	7	difference	difference	NOUN
cana-934	54	8	methods	method	NOUN
cana-934	54	9	(	(	PUNCT
cana-934	54	10	fdm	fdm	NOUN
cana-934	54	11	)	)	PUNCT
cana-934	54	12	for	for	ADP
cana-934	54	13	spatial	spatial	ADJ
cana-934	54	14	discretization	discretization	NOUN
cana-934	54	15	and	and	CCONJ
cana-934	54	16	time	time	NOUN
cana-934	54	17	-	-	PUNCT
cana-934	54	18	stepping	step	VERB
cana-934	54	19	algorithms	algorithm	NOUN
cana-934	54	20	for	for	ADP
cana-934	54	21	temporal	temporal	ADJ
cana-934	54	22	evolution	evolution	NOUN
cana-934	54	23	to	to	PART
cana-934	54	24	simulate	simulate	VERB
cana-934	54	25	the	the	DET
cana-934	54	26	dynamics	dynamic	NOUN
cana-934	54	27	governed	govern	VERB
cana-934	54	28	by	by	ADP
cana-934	54	29	the	the	DET
cana-934	54	30	qnlse	qnlse	PROPN
cana-934	54	31	.	.	PUNCT
cana-934	55	1	computational	computational	ADJ
cana-934	55	2	framework	framework	NOUN
cana-934	55	3	:	:	PUNCT
cana-934	55	4	•	•	NUM
cana-934	55	5	software	software	NOUN
cana-934	55	6	:	:	PUNCT
cana-934	55	7	the	the	DET
cana-934	55	8	simulations	simulation	NOUN
cana-934	55	9	are	be	AUX
cana-934	55	10	conducted	conduct	VERB
cana-934	55	11	using	use	VERB
cana-934	55	12	a	a	DET
cana-934	55	13	custom	custom	ADV
cana-934	55	14	-	-	PUNCT
cana-934	55	15	developed	develop	VERB
cana-934	55	16	code	code	NOUN
cana-934	55	17	in	in	ADP
cana-934	55	18	python	python	PROPN
cana-934	55	19	,	,	PUNCT
cana-934	55	20	leveraging	leverage	VERB
cana-934	55	21	libraries	library	NOUN
cana-934	55	22	such	such	ADJ
cana-934	55	23	as	as	ADP
cana-934	55	24	numpy	numpy	NOUN
cana-934	55	25	for	for	ADP
cana-934	55	26	efficient	efficient	ADJ
cana-934	55	27	numerical	numerical	ADJ
cana-934	55	28	operations	operation	NOUN
cana-934	55	29	and	and	CCONJ
cana-934	55	30	matplotlib	matplotlib	PROPN
cana-934	55	31	for	for	ADP
cana-934	55	32	visualization	visualization	NOUN
cana-934	55	33	.	.	PUNCT
cana-934	56	1	for	for	ADP
cana-934	56	2	certain	certain	ADJ
cana-934	56	3	computationally	computationally	ADV
cana-934	56	4	intensive	intensive	ADJ
cana-934	56	5	tasks	task	NOUN
cana-934	56	6	,	,	PUNCT
cana-934	56	7	we	we	PRON
cana-934	56	8	employ	employ	VERB
cana-934	56	9	parallel	parallel	ADJ
cana-934	56	10	computing	computing	NOUN
cana-934	56	11	techniques	technique	NOUN
cana-934	56	12	via	via	ADP
cana-934	56	13	the	the	DET
cana-934	56	14	mpi4py	mpi4py	PROPN
cana-934	56	15	library	library	NOUN
cana-934	56	16	to	to	PART
cana-934	56	17	enhance	enhance	VERB
cana-934	56	18	performance	performance	NOUN
cana-934	56	19	.	.	PUNCT
cana-934	57	1	•	•	NUM
cana-934	57	2	algorithms	algorithm	NOUN
cana-934	57	3	:	:	PUNCT
cana-934	57	4	the	the	DET
cana-934	57	5	crank	crank	NOUN
cana-934	57	6	-	-	PUNCT
cana-934	57	7	nicolson	nicolson	PROPN
cana-934	57	8	scheme	scheme	NOUN
cana-934	57	9	,	,	PUNCT
cana-934	57	10	known	know	VERB
cana-934	57	11	for	for	ADP
cana-934	57	12	its	its	PRON
cana-934	57	13	stability	stability	NOUN
cana-934	57	14	and	and	CCONJ
cana-934	57	15	accuracy	accuracy	NOUN
cana-934	57	16	,	,	PUNCT
cana-934	57	17	is	be	AUX
cana-934	57	18	employed	employ	VERB
cana-934	57	19	for	for	ADP
cana-934	57	20	time	time	NOUN
cana-934	57	21	integration	integration	NOUN
cana-934	57	22	,	,	PUNCT
cana-934	57	23	ensuring	ensure	VERB
cana-934	57	24	that	that	SCONJ
cana-934	57	25	the	the	DET
cana-934	57	26	discretized	discretized	ADJ
cana-934	57	27	version	version	NOUN
cana-934	57	28	of	of	ADP
cana-934	57	29	the	the	DET
cana-934	57	30	qnlse	qnlse	PROPN
cana-934	57	31	retains	retain	VERB
cana-934	57	32	its	its	PRON
cana-934	57	33	physical	physical	ADJ
cana-934	57	34	properties	property	NOUN
cana-934	57	35	over	over	ADP
cana-934	57	36	time	time	NOUN
cana-934	57	37	.	.	PUNCT
cana-934	58	1	for	for	ADP
cana-934	58	2	handling	handle	VERB
cana-934	58	3	nonlinear	nonlinear	ADJ
cana-934	58	4	and	and	CCONJ
cana-934	58	5	quantum	quantum	NOUN
cana-934	58	6	noise	noise	NOUN
cana-934	58	7	terms	term	NOUN
cana-934	58	8	,	,	PUNCT
cana-934	58	9	we	we	PRON
cana-934	58	10	incorporate	incorporate	VERB
cana-934	58	11	a	a	DET
cana-934	58	12	predictor	predictor	NOUN
cana-934	58	13	-	-	PUNCT
cana-934	58	14	corrector	corrector	NOUN
cana-934	58	15	approach	approach	NOUN
cana-934	58	16	,	,	PUNCT
cana-934	58	17	allowing	allow	VERB
cana-934	58	18	for	for	ADP
cana-934	58	19	an	an	DET
cana-934	58	20	adaptive	adaptive	ADJ
cana-934	58	21	timestep	timestep	NOUN
cana-934	58	22	that	that	PRON
cana-934	58	23	accommodates	accommodate	VERB
cana-934	58	24	the	the	DET
cana-934	58	25	varying	vary	VERB
cana-934	58	26	dynamics	dynamic	NOUN
cana-934	58	27	of	of	ADP
cana-934	58	28	the	the	DET
cana-934	58	29	system	system	NOUN
cana-934	58	30	.	.	PUNCT
cana-934	59	1	simulation	simulation	NOUN
cana-934	59	2	setup	setup	NOUN
cana-934	59	3	:	:	PUNCT
cana-934	59	4	•	•	ADP
cana-934	59	5	the	the	DET
cana-934	59	6	computational	computational	ADJ
cana-934	59	7	domain	domain	NOUN
cana-934	59	8	is	be	AUX
cana-934	59	9	discretized	discretize	VERB
cana-934	59	10	into	into	ADP
cana-934	59	11	a	a	DET
cana-934	59	12	uniform	uniform	ADJ
cana-934	59	13	grid	grid	NOUN
cana-934	59	14	with	with	ADP
cana-934	59	15	periodic	periodic	ADJ
cana-934	59	16	boundary	boundary	ADJ
cana-934	59	17	conditions	condition	NOUN
cana-934	59	18	to	to	PART
cana-934	59	19	model	model	VERB
cana-934	59	20	an	an	DET
cana-934	59	21	infinite	infinite	ADJ
cana-934	59	22	system	system	NOUN
cana-934	59	23	.	.	PUNCT
cana-934	60	1	initial	initial	ADJ
cana-934	60	2	conditions	condition	NOUN
cana-934	60	3	are	be	AUX
cana-934	60	4	chosen	choose	VERB
cana-934	60	5	to	to	PART
cana-934	60	6	represent	represent	VERB
cana-934	60	7	a	a	DET
cana-934	60	8	variety	variety	NOUN
cana-934	60	9	of	of	ADP
cana-934	60	10	physical	physical	ADJ
cana-934	60	11	scenarios	scenario	NOUN
cana-934	60	12	,	,	PUNCT
cana-934	60	13	from	from	ADP
cana-934	60	14	solitary	solitary	ADJ
cana-934	60	15	wave	wave	NOUN
cana-934	60	16	packets	packet	NOUN
cana-934	60	17	to	to	ADP
cana-934	60	18	random	random	ADJ
cana-934	60	19	quantum	quantum	NOUN
cana-934	60	20	fluctuations	fluctuation	NOUN
cana-934	60	21	.	.	PUNCT
cana-934	61	1	•	•	NUM
cana-934	61	2	a	a	DET
cana-934	61	3	series	series	NOUN
cana-934	61	4	of	of	ADP
cana-934	61	5	simulations	simulation	NOUN
cana-934	61	6	are	be	AUX
cana-934	61	7	performed	perform	VERB
cana-934	61	8	,	,	PUNCT
cana-934	61	9	systematically	systematically	ADV
cana-934	61	10	varying	vary	VERB
cana-934	61	11	the	the	DET
cana-934	61	12	coefficients	coefficient	NOUN
cana-934	61	13	and	and	CCONJ
cana-934	61	14	parameters	parameter	NOUN
cana-934	61	15	of	of	ADP
cana-934	61	16	the	the	DET
cana-934	61	17	qnlse	qnlse	NOUN
cana-934	61	18	to	to	PART
cana-934	61	19	explore	explore	VERB
cana-934	61	20	their	their	PRON
cana-934	61	21	impact	impact	NOUN
cana-934	61	22	on	on	ADP
cana-934	61	23	the	the	DET
cana-934	61	24	system	system	NOUN
cana-934	61	25	's	's	PART
cana-934	61	26	behavior	behavior	NOUN
cana-934	61	27	.	.	PUNCT
cana-934	62	1	this	this	PRON
cana-934	62	2	includes	include	VERB
cana-934	62	3	studies	study	NOUN
cana-934	62	4	on	on	ADP
cana-934	62	5	the	the	DET
cana-934	62	6	effect	effect	NOUN
cana-934	62	7	of	of	ADP
cana-934	62	8	time	time	NOUN
cana-934	62	9	-	-	PUNCT
cana-934	62	10	varying	vary	VERB
cana-934	62	11	coefficients	coefficient	NOUN
cana-934	62	12	,	,	PUNCT
cana-934	62	13	the	the	DET
cana-934	62	14	role	role	NOUN
cana-934	62	15	of	of	ADP
cana-934	62	16	quantum	quantum	ADJ
cana-934	62	17	noise	noise	NOUN
cana-934	62	18	intensity	intensity	NOUN
cana-934	62	19	,	,	PUNCT
cana-934	62	20	and	and	CCONJ
cana-934	62	21	the	the	DET
cana-934	62	22	dynamics	dynamic	NOUN
cana-934	62	23	of	of	ADP
cana-934	62	24	multi	multi	ADJ
cana-934	62	25	-	-	ADJ
cana-934	62	26	particle	particle	ADJ
cana-934	62	27	interactions	interaction	NOUN
cana-934	62	28	.	.	PUNCT
cana-934	63	1	through	through	ADP
cana-934	63	2	this	this	DET
cana-934	63	3	dual	dual	ADJ
cana-934	63	4	-	-	PUNCT
cana-934	63	5	pronged	pronged	ADJ
cana-934	63	6	approach	approach	NOUN
cana-934	63	7	of	of	ADP
cana-934	63	8	analytical	analytical	ADJ
cana-934	63	9	methods	method	NOUN
cana-934	63	10	and	and	CCONJ
cana-934	63	11	numerical	numerical	ADJ
cana-934	63	12	simulations	simulation	NOUN
cana-934	63	13	,	,	PUNCT
cana-934	63	14	our	our	PRON
cana-934	63	15	research	research	NOUN
cana-934	63	16	aims	aim	VERB
cana-934	63	17	to	to	PART
cana-934	63	18	provide	provide	VERB
cana-934	63	19	a	a	DET
cana-934	63	20	deep	deep	ADJ
cana-934	63	21	and	and	CCONJ
cana-934	63	22	comprehensive	comprehensive	ADJ
cana-934	63	23	analysis	analysis	NOUN
cana-934	63	24	of	of	ADP
cana-934	63	25	the	the	DET
cana-934	63	26	qnlse	qnlse	NOUN
cana-934	63	27	,	,	PUNCT
cana-934	63	28	shedding	shed	VERB
cana-934	63	29	light	light	NOUN
cana-934	63	30	on	on	ADP
cana-934	63	31	the	the	DET
cana-934	63	32	nuanced	nuanced	ADJ
cana-934	63	33	communications	communication	NOUN
cana-934	63	34	on	on	ADP
cana-934	63	35	applied	apply	VERB
cana-934	63	36	nonlinear	nonlinear	ADJ
cana-934	63	37	analysis	analysis	NOUN
cana-934	63	38	issn	issn	NOUN
cana-934	63	39	:	:	PUNCT
cana-934	63	40	1074	1074	NUM
cana-934	63	41	-	-	PUNCT
cana-934	63	42	133x	133x	NUM
cana-934	63	43	vol	vol	NOUN
cana-934	63	44	31	31	NUM
cana-934	63	45	no	no	NOUN
cana-934	63	46	.	.	PUNCT
cana-934	64	1	4s	4s	NUM
cana-934	64	2	(	(	PUNCT
cana-934	64	3	2024	2024	NUM
cana-934	64	4	)	)	PUNCT
cana-934	64	5	414	414	NUM
cana-934	64	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-934	64	7	dynamics	dynamic	NOUN
cana-934	64	8	of	of	ADP
cana-934	64	9	quantum	quantum	NOUN
cana-934	64	10	systems	system	NOUN
cana-934	64	11	described	describe	VERB
cana-934	64	12	by	by	ADP
cana-934	64	13	this	this	DET
cana-934	64	14	advanced	advanced	ADJ
cana-934	64	15	mathematical	mathematical	ADJ
cana-934	64	16	model	model	NOUN
cana-934	64	17	.	.	PUNCT
cana-934	65	1	the	the	DET
cana-934	65	2	integration	integration	NOUN
cana-934	65	3	of	of	ADP
cana-934	65	4	theory	theory	NOUN
cana-934	65	5	with	with	ADP
cana-934	65	6	computational	computational	ADJ
cana-934	65	7	insights	insight	NOUN
cana-934	65	8	enables	enable	VERB
cana-934	65	9	us	we	PRON
cana-934	65	10	to	to	PART
cana-934	65	11	navigate	navigate	VERB
cana-934	65	12	the	the	DET
cana-934	65	13	complex	complex	ADJ
cana-934	65	14	landscape	landscape	NOUN
cana-934	65	15	of	of	ADP
cana-934	65	16	quantum	quantum	ADJ
cana-934	65	17	mechanics	mechanic	NOUN
cana-934	65	18	,	,	PUNCT
cana-934	65	19	offering	offer	VERB
cana-934	65	20	new	new	ADJ
cana-934	65	21	perspectives	perspective	NOUN
cana-934	65	22	on	on	ADP
cana-934	65	23	stability	stability	NOUN
cana-934	65	24	,	,	PUNCT
cana-934	65	25	decay	decay	NOUN
cana-934	65	26	,	,	PUNCT
cana-934	65	27	and	and	CCONJ
cana-934	65	28	interaction	interaction	NOUN
cana-934	65	29	phenomena	phenomenon	NOUN
cana-934	65	30	within	within	ADP
cana-934	65	31	these	these	DET
cana-934	65	32	systems	system	NOUN
cana-934	65	33	.	.	PUNCT
cana-934	66	1	iv	iv	X
cana-934	66	2	.	.	PUNCT
cana-934	66	3	results	result	NOUN
cana-934	66	4	and	and	CCONJ
cana-934	66	5	discussion	discussion	VERB
cana-934	66	6	our	our	PRON
cana-934	66	7	investigation	investigation	NOUN
cana-934	66	8	into	into	ADP
cana-934	66	9	the	the	DET
cana-934	66	10	quantum	quantum	NOUN
cana-934	66	11	noise	noise	NOUN
cana-934	66	12	-	-	PUNCT
cana-934	66	13	extended	extend	VERB
cana-934	66	14	nonlinear	nonlinear	ADJ
cana-934	66	15	schrödinger	schrödinger	ADJ
cana-934	66	16	equation	equation	NOUN
cana-934	66	17	(	(	PUNCT
cana-934	66	18	qnlse	qnlse	PROPN
cana-934	66	19	)	)	PUNCT
cana-934	66	20	has	have	AUX
cana-934	66	21	yielded	yield	VERB
cana-934	66	22	insightful	insightful	ADJ
cana-934	66	23	findings	finding	NOUN
cana-934	66	24	across	across	ADP
cana-934	66	25	three	three	NUM
cana-934	66	26	primary	primary	ADJ
cana-934	66	27	areas	area	NOUN
cana-934	66	28	:	:	PUNCT
cana-934	66	29	quantum	quantum	NOUN
cana-934	66	30	chaos	chaos	NOUN
cana-934	66	31	,	,	PUNCT
cana-934	66	32	soliton	soliton	NOUN
cana-934	66	33	dynamics	dynamic	NOUN
cana-934	66	34	,	,	PUNCT
cana-934	66	35	and	and	CCONJ
cana-934	66	36	quantum	quantum	ADJ
cana-934	66	37	turbulence	turbulence	NOUN
cana-934	66	38	.	.	PUNCT
cana-934	67	1	this	this	DET
cana-934	67	2	section	section	NOUN
cana-934	67	3	delineates	delineate	VERB
cana-934	67	4	these	these	DET
cana-934	67	5	findings	finding	NOUN
cana-934	67	6	,	,	PUNCT
cana-934	67	7	supported	support	VERB
cana-934	67	8	by	by	ADP
cana-934	67	9	analytical	analytical	ADJ
cana-934	67	10	insights	insight	NOUN
cana-934	67	11	,	,	PUNCT
cana-934	67	12	numerical	numerical	ADJ
cana-934	67	13	data	datum	NOUN
cana-934	67	14	,	,	PUNCT
cana-934	67	15	and	and	CCONJ
cana-934	67	16	visual	visual	ADJ
cana-934	67	17	representations	representation	NOUN
cana-934	67	18	.	.	PUNCT
cana-934	68	1	quantum	quantum	ADJ
cana-934	68	2	chaos	chaos	NOUN
cana-934	68	3	findings	finding	NOUN
cana-934	68	4	:	:	PUNCT
cana-934	68	5	our	our	PRON
cana-934	68	6	analysis	analysis	NOUN
cana-934	68	7	reveals	reveal	VERB
cana-934	68	8	that	that	SCONJ
cana-934	68	9	quantum	quantum	NOUN
cana-934	68	10	systems	system	NOUN
cana-934	68	11	governed	govern	VERB
cana-934	68	12	by	by	ADP
cana-934	68	13	the	the	DET
cana-934	68	14	qnlse	qnlse	PROPN
cana-934	68	15	exhibit	exhibit	VERB
cana-934	68	16	chaotic	chaotic	ADJ
cana-934	68	17	behavior	behavior	NOUN
cana-934	68	18	under	under	ADP
cana-934	68	19	specific	specific	ADJ
cana-934	68	20	conditions	condition	NOUN
cana-934	68	21	,	,	PUNCT
cana-934	68	22	notably	notably	ADV
cana-934	68	23	when	when	SCONJ
cana-934	68	24	the	the	DET
cana-934	68	25	interaction	interaction	NOUN
cana-934	68	26	between	between	ADP
cana-934	68	27	quantum	quantum	NOUN
cana-934	68	28	noise	noise	NOUN
cana-934	68	29	and	and	CCONJ
cana-934	68	30	nonlinearity	nonlinearity	NOUN
cana-934	68	31	surpasses	surpass	VERB
cana-934	68	32	a	a	DET
cana-934	68	33	critical	critical	ADJ
cana-934	68	34	threshold	threshold	NOUN
cana-934	68	35	.	.	PUNCT
cana-934	69	1	this	this	DET
cana-934	69	2	chaos	chaos	NOUN
cana-934	69	3	manifests	manifest	VERB
cana-934	69	4	as	as	ADP
cana-934	69	5	unpredictable	unpredictable	ADJ
cana-934	69	6	fluctuations	fluctuation	NOUN
cana-934	69	7	in	in	ADP
cana-934	69	8	the	the	DET
cana-934	69	9	wave	wave	NOUN
cana-934	69	10	function	function	NOUN
cana-934	69	11	amplitude	amplitude	NOUN
cana-934	69	12	and	and	CCONJ
cana-934	69	13	phase	phase	NOUN
cana-934	69	14	,	,	PUNCT
cana-934	69	15	deviating	deviate	VERB
cana-934	69	16	significantly	significantly	ADV
cana-934	69	17	from	from	ADP
cana-934	69	18	classical	classical	ADJ
cana-934	69	19	predictions	prediction	NOUN
cana-934	69	20	.	.	PUNCT
cana-934	70	1	equation	equation	NOUN
cana-934	70	2	:	:	PUNCT
cana-934	70	3	the	the	DET
cana-934	70	4	lyapunov	lyapunov	ADJ
cana-934	70	5	exponent	exponent	NOUN
cana-934	70	6	,	,	PUNCT
cana-934	70	7	λ	λ	PROPN
cana-934	70	8	,	,	PUNCT
cana-934	70	9	a	a	DET
cana-934	70	10	measure	measure	NOUN
cana-934	70	11	of	of	ADP
cana-934	70	12	chaos	chaos	NOUN
cana-934	70	13	,	,	PUNCT
cana-934	70	14	was	be	AUX
cana-934	70	15	calculated	calculate	VERB
cana-934	70	16	using	use	VERB
cana-934	70	17	the	the	DET
cana-934	70	18	relation	relation	NOUN
cana-934	70	19	:	:	PUNCT
cana-934	70	20	𝜆	𝜆	X
cana-934	70	21	=	=	SYM
cana-934	70	22	𝑙𝑖𝑚𝑡	𝑙𝑖𝑚𝑡	NOUN
cana-934	70	23	→	→	SYM
cana-934	70	24	∞	∞	NUM
cana-934	70	25	1	1	NUM
cana-934	70	26	𝑡	𝑡	SYM
cana-934	70	27	ln	ln	ADJ
cana-934	70	28	(	(	PUNCT
cana-934	70	29	∣	∣	PROPN
cana-934	70	30	𝛿𝜓(𝑡	𝛿𝜓(𝑡	PRON
cana-934	70	31	)	)	PUNCT
cana-934	70	32	∣	∣	ADJ
cana-934	70	33	∣	∣	ADJ
cana-934	70	34	𝛿𝜓(0	𝛿𝜓(0	PROPN
cana-934	70	35	)	)	PUNCT
cana-934	70	36	∣	∣	NOUN
cana-934	70	37	)	)	PUNCT
cana-934	70	38	,	,	PUNCT
cana-934	70	39	where	where	SCONJ
cana-934	70	40	∣δψ(t)∣	∣δψ(t)∣	NOUN
cana-934	70	41	represents	represent	VERB
cana-934	70	42	the	the	DET
cana-934	70	43	deviation	deviation	NOUN
cana-934	70	44	of	of	ADP
cana-934	70	45	the	the	DET
cana-934	70	46	wave	wave	NOUN
cana-934	70	47	function	function	NOUN
cana-934	70	48	from	from	ADP
cana-934	70	49	its	its	PRON
cana-934	70	50	initial	initial	ADJ
cana-934	70	51	state	state	NOUN
cana-934	70	52	over	over	ADP
cana-934	70	53	time	time	NOUN
cana-934	70	54	.	.	PUNCT
cana-934	71	1	table	table	NOUN
cana-934	71	2	1	1	NUM
cana-934	71	3	:	:	PUNCT
cana-934	71	4	lyapunov	lyapunov	NOUN
cana-934	71	5	exponents	exponent	NOUN
cana-934	71	6	for	for	ADP
cana-934	71	7	varying	vary	VERB
cana-934	71	8	parameters	parameter	NOUN
cana-934	71	9	parameter	parameter	NOUN
cana-934	71	10	set	set	VERB
cana-934	71	11	lyapunov	lyapunov	PROPN
cana-934	71	12	exponent	exponent	NOUN
cana-934	71	13	(	(	PUNCT
cana-934	71	14	λ	λ	NOUN
cana-934	71	15	)	)	PUNCT
cana-934	71	16	chaotic	chaotic	ADJ
cana-934	71	17	behavior	behavior	NOUN
cana-934	71	18	a	a	DET
cana-934	71	19	0.02	0.02	NUM
cana-934	71	20	absent	absent	ADJ
cana-934	71	21	b	b	NUM
cana-934	71	22	0.15	0.15	NUM
cana-934	71	23	present	present	ADJ
cana-934	71	24	discussion	discussion	NOUN
cana-934	71	25	:	:	PUNCT
cana-934	71	26	the	the	DET
cana-934	71	27	presence	presence	NOUN
cana-934	71	28	of	of	ADP
cana-934	71	29	quantum	quantum	NOUN
cana-934	71	30	chaos	chaos	NOUN
cana-934	71	31	was	be	AUX
cana-934	71	32	closely	closely	ADV
cana-934	71	33	tied	tie	VERB
cana-934	71	34	to	to	ADP
cana-934	71	35	the	the	DET
cana-934	71	36	time	time	NOUN
cana-934	71	37	-	-	PUNCT
cana-934	71	38	dependency	dependency	NOUN
cana-934	71	39	of	of	ADP
cana-934	71	40	the	the	DET
cana-934	71	41	system	system	NOUN
cana-934	71	42	's	's	PART
cana-934	71	43	coefficients	coefficient	NOUN
cana-934	71	44	and	and	CCONJ
cana-934	71	45	the	the	DET
cana-934	71	46	strength	strength	NOUN
cana-934	71	47	of	of	ADP
cana-934	71	48	quantum	quantum	NOUN
cana-934	71	49	noise	noise	NOUN
cana-934	71	50	.	.	PUNCT
cana-934	72	1	parameter	parameter	PROPN
cana-934	72	2	set	set	PROPN
cana-934	72	3	b	b	PROPN
cana-934	72	4	,	,	PUNCT
cana-934	72	5	which	which	PRON
cana-934	72	6	exhibited	exhibit	VERB
cana-934	72	7	a	a	DET
cana-934	72	8	higher	high	ADJ
cana-934	72	9	lyapunov	lyapunov	NOUN
cana-934	72	10	exponent	exponent	NOUN
cana-934	72	11	,	,	PUNCT
cana-934	72	12	indicated	indicate	VERB
cana-934	72	13	a	a	DET
cana-934	72	14	transition	transition	NOUN
cana-934	72	15	to	to	ADP
cana-934	72	16	chaotic	chaotic	ADJ
cana-934	72	17	dynamics	dynamic	NOUN
cana-934	72	18	,	,	PUNCT
cana-934	72	19	underscoring	underscore	VERB
cana-934	72	20	the	the	DET
cana-934	72	21	critical	critical	ADJ
cana-934	72	22	role	role	NOUN
cana-934	72	23	of	of	ADP
cana-934	72	24	quantum	quantum	NOUN
cana-934	72	25	noise	noise	NOUN
cana-934	72	26	in	in	ADP
cana-934	72	27	facilitating	facilitate	VERB
cana-934	72	28	such	such	ADJ
cana-934	72	29	behavior	behavior	NOUN
cana-934	72	30	.	.	PUNCT
cana-934	73	1	soliton	soliton	NOUN
cana-934	73	2	dynamics	dynamic	NOUN
cana-934	73	3	findings	finding	NOUN
cana-934	73	4	:	:	PUNCT
cana-934	73	5	the	the	DET
cana-934	73	6	study	study	NOUN
cana-934	73	7	unveiled	unveil	VERB
cana-934	73	8	that	that	SCONJ
cana-934	73	9	solitons	soliton	NOUN
cana-934	73	10	within	within	ADP
cana-934	73	11	the	the	DET
cana-934	73	12	qnlse	qnlse	ADJ
cana-934	73	13	framework	framework	NOUN
cana-934	73	14	maintain	maintain	VERB
cana-934	73	15	their	their	PRON
cana-934	73	16	coherence	coherence	NOUN
cana-934	73	17	over	over	ADP
cana-934	73	18	remarkably	remarkably	ADV
cana-934	73	19	long	long	ADJ
cana-934	73	20	distances	distance	NOUN
cana-934	73	21	and	and	CCONJ
cana-934	73	22	times	time	NOUN
cana-934	73	23	,	,	PUNCT
cana-934	73	24	even	even	ADV
cana-934	73	25	in	in	ADP
cana-934	73	26	the	the	DET
cana-934	73	27	presence	presence	NOUN
cana-934	73	28	of	of	ADP
cana-934	73	29	quantum	quantum	NOUN
cana-934	73	30	noise	noise	NOUN
cana-934	73	31	and	and	CCONJ
cana-934	73	32	multi	multi	ADJ
cana-934	73	33	-	-	ADJ
cana-934	73	34	particle	particle	ADJ
cana-934	73	35	interactions	interaction	NOUN
cana-934	73	36	.	.	PUNCT
cana-934	74	1	however	however	ADV
cana-934	74	2	,	,	PUNCT
cana-934	74	3	their	their	PRON
cana-934	74	4	stability	stability	NOUN
cana-934	74	5	is	be	AUX
cana-934	74	6	highly	highly	ADV
cana-934	74	7	sensitive	sensitive	ADJ
cana-934	74	8	to	to	ADP
cana-934	74	9	the	the	DET
cana-934	74	10	specific	specific	ADJ
cana-934	74	11	form	form	NOUN
cana-934	74	12	of	of	ADP
cana-934	74	13	time	time	NOUN
cana-934	74	14	-	-	PUNCT
cana-934	74	15	dependent	dependent	ADJ
cana-934	74	16	coefficients	coefficient	NOUN
cana-934	74	17	.	.	PUNCT
cana-934	75	1	equation	equation	NOUN
cana-934	75	2	:	:	PUNCT
cana-934	75	3	the	the	DET
cana-934	75	4	stability	stability	NOUN
cana-934	75	5	criterion	criterion	NOUN
cana-934	75	6	for	for	ADP
cana-934	75	7	solitons	soliton	NOUN
cana-934	75	8	was	be	AUX
cana-934	75	9	derived	derive	VERB
cana-934	75	10	from	from	ADP
cana-934	75	11	the	the	DET
cana-934	75	12	modified	modify	VERB
cana-934	75	13	energy	energy	NOUN
cana-934	75	14	balance	balance	NOUN
cana-934	75	15	equation	equation	NOUN
cana-934	75	16	:	:	PUNCT
cana-934	75	17	𝐸	𝐸	PROPN
cana-934	75	18	=	=	SYM
cana-934	75	19	∫	∫	PROPN
cana-934	75	20	(	(	PUNCT
cana-934	75	21	∣∣	∣∣	NUM
cana-934	75	22	∣	∣	ADJ
cana-934	75	23	𝛻𝜓	𝛻𝜓	PUNCT
cana-934	75	24	∣2	∣2	NOUN
cana-934	75	25	+	+	X
cana-934	75	26	𝑉(𝑥	𝑉(𝑥	PROPN
cana-934	75	27	,	,	PUNCT
cana-934	75	28	𝑡	𝑡	PROPN
cana-934	75	29	)	)	PUNCT
cana-934	75	30	∣∣	∣∣	NUM
cana-934	75	31	∣	∣	ADJ
cana-934	75	32	𝜓	𝜓	NOUN
cana-934	75	33	∣2	∣2	ADJ
cana-934	75	34	+	+	CCONJ
cana-934	75	35	1	1	NUM
cana-934	75	36	2	2	NUM
cana-934	75	37	𝑔	𝑔	PROPN
cana-934	75	38	∣∣	∣∣	NUM
cana-934	75	39	∣	∣	ADJ
cana-934	75	40	𝜓	𝜓	NOUN
cana-934	75	41	∣4	∣4	NOUN
cana-934	75	42	)	)	PUNCT
cana-934	75	43	𝑑𝑥	𝑑𝑥	VERB
cana-934	75	44	,	,	PUNCT
cana-934	75	45	indicating	indicate	VERB
cana-934	75	46	that	that	SCONJ
cana-934	75	47	soliton	soliton	NOUN
cana-934	75	48	stability	stability	NOUN
cana-934	75	49	is	be	AUX
cana-934	75	50	contingent	contingent	ADJ
cana-934	75	51	upon	upon	SCONJ
cana-934	75	52	the	the	DET
cana-934	75	53	conservation	conservation	NOUN
cana-934	75	54	of	of	ADP
cana-934	75	55	this	this	DET
cana-934	75	56	modified	modify	VERB
cana-934	75	57	energy	energy	NOUN
cana-934	75	58	in	in	ADP
cana-934	75	59	the	the	DET
cana-934	75	60	system	system	NOUN
cana-934	75	61	.	.	PUNCT
cana-934	76	1	communications	communication	NOUN
cana-934	76	2	on	on	ADP
cana-934	76	3	applied	apply	VERB
cana-934	76	4	nonlinear	nonlinear	ADJ
cana-934	76	5	analysis	analysis	NOUN
cana-934	76	6	issn	issn	NOUN
cana-934	76	7	:	:	PUNCT
cana-934	76	8	1074	1074	NUM
cana-934	76	9	-	-	PUNCT
cana-934	76	10	133x	133x	NUM
cana-934	76	11	vol	vol	NOUN
cana-934	76	12	31	31	NUM
cana-934	76	13	no	no	NOUN
cana-934	76	14	.	.	PUNCT
cana-934	77	1	4s	4s	NUM
cana-934	77	2	(	(	PUNCT
cana-934	77	3	2024	2024	NUM
cana-934	77	4	)	)	PUNCT
cana-934	78	1	415	415	NUM
cana-934	78	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-934	78	3	implications	implication	NOUN
cana-934	78	4	for	for	ADP
cana-934	78	5	quantum	quantum	NOUN
cana-934	78	6	computing	computing	NOUN
cana-934	78	7	and	and	CCONJ
cana-934	78	8	simulation	simulation	NOUN
cana-934	78	9	our	our	PRON
cana-934	78	10	exploration	exploration	NOUN
cana-934	78	11	into	into	ADP
cana-934	78	12	the	the	DET
cana-934	78	13	quantum	quantum	NOUN
cana-934	78	14	noise	noise	NOUN
cana-934	78	15	-	-	PUNCT
cana-934	78	16	extended	extend	VERB
cana-934	78	17	nonlinear	nonlinear	ADJ
cana-934	78	18	schrödinger	schrödinger	ADJ
cana-934	78	19	equation	equation	NOUN
cana-934	78	20	(	(	PUNCT
cana-934	78	21	qnlse	qnlse	PROPN
cana-934	78	22	)	)	PUNCT
cana-934	78	23	and	and	CCONJ
cana-934	78	24	its	its	PRON
cana-934	78	25	intricate	intricate	ADJ
cana-934	78	26	dynamics	dynamic	NOUN
cana-934	78	27	—	—	PUNCT
cana-934	78	28	spanning	span	VERB
cana-934	78	29	quantum	quantum	ADJ
cana-934	78	30	chaos	chaos	NOUN
cana-934	78	31	,	,	PUNCT
cana-934	78	32	soliton	soliton	NOUN
cana-934	78	33	stability	stability	NOUN
cana-934	78	34	,	,	PUNCT
cana-934	78	35	and	and	CCONJ
cana-934	78	36	quantum	quantum	ADJ
cana-934	78	37	turbulence	turbulence	NOUN
cana-934	78	38	—	—	PUNCT
cana-934	78	39	holds	hold	VERB
cana-934	78	40	profound	profound	ADJ
cana-934	78	41	implications	implication	NOUN
cana-934	78	42	for	for	ADP
cana-934	78	43	the	the	DET
cana-934	78	44	realm	realm	NOUN
cana-934	78	45	of	of	ADP
cana-934	78	46	quantum	quantum	NOUN
cana-934	78	47	computing	computing	NOUN
cana-934	78	48	and	and	CCONJ
cana-934	78	49	simulation	simulation	NOUN
cana-934	78	50	.	.	PUNCT
cana-934	79	1	these	these	DET
cana-934	79	2	findings	finding	NOUN
cana-934	79	3	not	not	PART
cana-934	79	4	only	only	ADV
cana-934	79	5	deepen	deepen	VERB
cana-934	79	6	our	our	PRON
cana-934	79	7	understanding	understanding	NOUN
cana-934	79	8	of	of	ADP
cana-934	79	9	quantum	quantum	NOUN
cana-934	79	10	systems	system	NOUN
cana-934	79	11	but	but	CCONJ
cana-934	79	12	also	also	ADV
cana-934	79	13	pave	pave	VERB
cana-934	79	14	the	the	DET
cana-934	79	15	way	way	NOUN
cana-934	79	16	for	for	ADP
cana-934	79	17	innovative	innovative	ADJ
cana-934	79	18	applications	application	NOUN
cana-934	79	19	in	in	ADP
cana-934	79	20	quantum	quantum	ADJ
cana-934	79	21	technologies	technology	NOUN
cana-934	79	22	.	.	PUNCT
cana-934	80	1	the	the	DET
cana-934	80	2	discovery	discovery	NOUN
cana-934	80	3	of	of	ADP
cana-934	80	4	chaos	chaos	NOUN
cana-934	80	5	in	in	ADP
cana-934	80	6	quantum	quantum	ADJ
cana-934	80	7	systems	system	NOUN
cana-934	80	8	,	,	PUNCT
cana-934	80	9	as	as	SCONJ
cana-934	80	10	governed	govern	VERB
cana-934	80	11	by	by	ADP
cana-934	80	12	the	the	DET
cana-934	80	13	qnlse	qnlse	NOUN
cana-934	80	14	,	,	PUNCT
cana-934	80	15	underscores	underscore	VERB
cana-934	80	16	the	the	DET
cana-934	80	17	sensitivity	sensitivity	NOUN
cana-934	80	18	of	of	ADP
cana-934	80	19	quantum	quantum	ADJ
cana-934	80	20	states	state	NOUN
cana-934	80	21	to	to	ADP
cana-934	80	22	initial	initial	ADJ
cana-934	80	23	conditions	condition	NOUN
cana-934	80	24	and	and	CCONJ
cana-934	80	25	noise	noise	NOUN
cana-934	80	26	,	,	PUNCT
cana-934	80	27	which	which	PRON
cana-934	80	28	is	be	AUX
cana-934	80	29	a	a	DET
cana-934	80	30	double	double	ADJ
cana-934	80	31	-	-	PUNCT
cana-934	80	32	edged	edge	VERB
cana-934	80	33	sword	sword	NOUN
cana-934	80	34	for	for	ADP
cana-934	80	35	quantum	quantum	NOUN
cana-934	80	36	computing	computing	NOUN
cana-934	80	37	.	.	PUNCT
cana-934	81	1	on	on	ADP
cana-934	81	2	one	one	NUM
cana-934	81	3	hand	hand	NOUN
cana-934	81	4	,	,	PUNCT
cana-934	81	5	this	this	DET
cana-934	81	6	sensitivity	sensitivity	NOUN
cana-934	81	7	can	can	AUX
cana-934	81	8	lead	lead	VERB
cana-934	81	9	to	to	ADP
cana-934	81	10	challenges	challenge	NOUN
cana-934	81	11	in	in	ADP
cana-934	81	12	maintaining	maintain	VERB
cana-934	81	13	coherence	coherence	NOUN
cana-934	81	14	and	and	CCONJ
cana-934	81	15	fidelity	fidelity	NOUN
cana-934	81	16	in	in	ADP
cana-934	81	17	quantum	quantum	NOUN
cana-934	81	18	computations	computation	NOUN
cana-934	81	19	.	.	PUNCT
cana-934	82	1	on	on	ADP
cana-934	82	2	the	the	DET
cana-934	82	3	other	other	ADJ
cana-934	82	4	hand	hand	NOUN
cana-934	82	5	,	,	PUNCT
cana-934	82	6	it	it	PRON
cana-934	82	7	opens	open	VERB
cana-934	82	8	up	up	ADP
cana-934	82	9	new	new	ADJ
cana-934	82	10	avenues	avenue	NOUN
cana-934	82	11	for	for	ADP
cana-934	82	12	designing	design	VERB
cana-934	82	13	quantum	quantum	ADJ
cana-934	82	14	algorithms	algorithm	NOUN
cana-934	82	15	based	base	VERB
cana-934	82	16	on	on	ADP
cana-934	82	17	chaotic	chaotic	ADJ
cana-934	82	18	dynamics	dynamic	NOUN
cana-934	82	19	,	,	PUNCT
cana-934	82	20	potentially	potentially	ADV
cana-934	82	21	enhancing	enhance	VERB
cana-934	82	22	the	the	DET
cana-934	82	23	efficiency	efficiency	NOUN
cana-934	82	24	of	of	ADP
cana-934	82	25	solving	solve	VERB
cana-934	82	26	complex	complex	ADJ
cana-934	82	27	problems	problem	NOUN
cana-934	82	28	that	that	PRON
cana-934	82	29	are	be	AUX
cana-934	82	30	intractable	intractable	ADJ
cana-934	82	31	for	for	ADP
cana-934	82	32	classical	classical	ADJ
cana-934	82	33	computers	computer	NOUN
cana-934	82	34	.	.	PUNCT
cana-934	83	1	furthermore	furthermore	ADV
cana-934	83	2	,	,	PUNCT
cana-934	83	3	the	the	DET
cana-934	83	4	ability	ability	NOUN
cana-934	83	5	to	to	PART
cana-934	83	6	characterize	characterize	VERB
cana-934	83	7	and	and	CCONJ
cana-934	83	8	control	control	NOUN
cana-934	83	9	chaos	chaos	NOUN
cana-934	83	10	could	could	AUX
cana-934	83	11	lead	lead	VERB
cana-934	83	12	to	to	ADP
cana-934	83	13	robust	robust	ADJ
cana-934	83	14	methods	method	NOUN
cana-934	83	15	for	for	ADP
cana-934	83	16	error	error	NOUN
cana-934	83	17	correction	correction	NOUN
cana-934	83	18	and	and	CCONJ
cana-934	83	19	the	the	DET
cana-934	83	20	development	development	NOUN
cana-934	83	21	of	of	ADP
cana-934	83	22	chaos	chaos	NOUN
cana-934	83	23	-	-	PUNCT
cana-934	83	24	based	base	VERB
cana-934	83	25	quantum	quantum	ADJ
cana-934	83	26	cryptographic	cryptographic	ADJ
cana-934	83	27	systems	system	NOUN
cana-934	83	28	,	,	PUNCT
cana-934	83	29	enhancing	enhance	VERB
cana-934	83	30	the	the	DET
cana-934	83	31	security	security	NOUN
cana-934	83	32	of	of	ADP
cana-934	83	33	quantum	quantum	ADJ
cana-934	83	34	communication	communication	NOUN
cana-934	83	35	.	.	PUNCT
cana-934	84	1	the	the	DET
cana-934	84	2	stability	stability	NOUN
cana-934	84	3	of	of	ADP
cana-934	84	4	solitons	soliton	NOUN
cana-934	84	5	in	in	ADP
cana-934	84	6	the	the	DET
cana-934	84	7	presence	presence	NOUN
cana-934	84	8	of	of	ADP
cana-934	84	9	quantum	quantum	NOUN
cana-934	84	10	noise	noise	NOUN
cana-934	84	11	and	and	CCONJ
cana-934	84	12	interactions	interaction	NOUN
cana-934	84	13	reveals	reveal	VERB
cana-934	84	14	the	the	DET
cana-934	84	15	potential	potential	NOUN
cana-934	84	16	for	for	ADP
cana-934	84	17	utilizing	utilize	VERB
cana-934	84	18	soliton	soliton	NOUN
cana-934	84	19	-	-	PUNCT
cana-934	84	20	like	like	ADJ
cana-934	84	21	states	state	NOUN
cana-934	84	22	in	in	ADP
cana-934	84	23	quantum	quantum	ADJ
cana-934	84	24	information	information	NOUN
cana-934	84	25	processing	processing	NOUN
cana-934	84	26	.	.	PUNCT
cana-934	85	1	solitons	soliton	NOUN
cana-934	85	2	,	,	PUNCT
cana-934	85	3	due	due	ADP
cana-934	85	4	to	to	ADP
cana-934	85	5	their	their	PRON
cana-934	85	6	inherent	inherent	ADJ
cana-934	85	7	robustness	robustness	NOUN
cana-934	85	8	,	,	PUNCT
cana-934	85	9	could	could	AUX
cana-934	85	10	serve	serve	VERB
cana-934	85	11	as	as	ADP
cana-934	85	12	stable	stable	ADJ
cana-934	85	13	carriers	carrier	NOUN
cana-934	85	14	of	of	ADP
cana-934	85	15	quantum	quantum	ADJ
cana-934	85	16	information	information	NOUN
cana-934	85	17	,	,	PUNCT
cana-934	85	18	facilitating	facilitate	VERB
cana-934	85	19	long	long	ADJ
cana-934	85	20	-	-	PUNCT
cana-934	85	21	distance	distance	NOUN
cana-934	85	22	quantum	quantum	ADJ
cana-934	85	23	communication	communication	NOUN
cana-934	85	24	with	with	ADP
cana-934	85	25	minimal	minimal	ADJ
cana-934	85	26	loss	loss	NOUN
cana-934	85	27	.	.	PUNCT
cana-934	86	1	moreover	moreover	ADV
cana-934	86	2	,	,	PUNCT
cana-934	86	3	the	the	DET
cana-934	86	4	interactions	interaction	NOUN
cana-934	86	5	between	between	ADP
cana-934	86	6	solitons	soliton	NOUN
cana-934	86	7	might	might	AUX
cana-934	86	8	be	be	AUX
cana-934	86	9	harnessed	harness	VERB
cana-934	86	10	to	to	PART
cana-934	86	11	perform	perform	VERB
cana-934	86	12	quantum	quantum	ADJ
cana-934	86	13	logic	logic	NOUN
cana-934	86	14	operations	operation	NOUN
cana-934	86	15	,	,	PUNCT
cana-934	86	16	serving	serve	VERB
cana-934	86	17	as	as	ADP
cana-934	86	18	a	a	DET
cana-934	86	19	basis	basis	NOUN
cana-934	86	20	for	for	ADP
cana-934	86	21	soliton	soliton	NOUN
cana-934	86	22	-	-	PUNCT
cana-934	86	23	based	base	VERB
cana-934	86	24	quantum	quantum	ADJ
cana-934	86	25	computation	computation	NOUN
cana-934	86	26	models	model	NOUN
cana-934	86	27	.	.	PUNCT
cana-934	87	1	this	this	PRON
cana-934	87	2	opens	open	VERB
cana-934	87	3	a	a	DET
cana-934	87	4	novel	novel	ADJ
cana-934	87	5	paradigm	paradigm	NOUN
cana-934	87	6	for	for	ADP
cana-934	87	7	quantum	quantum	NOUN
cana-934	87	8	computing	computing	NOUN
cana-934	87	9	architectures	architecture	NOUN
cana-934	87	10	that	that	PRON
cana-934	87	11	leverage	leverage	VERB
cana-934	87	12	the	the	DET
cana-934	87	13	unique	unique	ADJ
cana-934	87	14	properties	property	NOUN
cana-934	87	15	of	of	ADP
cana-934	87	16	solitons	soliton	NOUN
cana-934	87	17	for	for	ADP
cana-934	87	18	both	both	DET
cana-934	87	19	computation	computation	NOUN
cana-934	87	20	and	and	CCONJ
cana-934	87	21	communication	communication	NOUN
cana-934	87	22	within	within	ADP
cana-934	87	23	quantum	quantum	ADJ
cana-934	87	24	networks	network	NOUN
cana-934	87	25	.	.	PUNCT
cana-934	88	1	lastly	lastly	ADV
cana-934	88	2	,	,	PUNCT
cana-934	88	3	the	the	DET
cana-934	88	4	emergence	emergence	NOUN
cana-934	88	5	of	of	ADP
cana-934	88	6	quantum	quantum	ADJ
cana-934	88	7	turbulence	turbulence	NOUN
cana-934	88	8	and	and	CCONJ
cana-934	88	9	the	the	DET
cana-934	88	10	associated	associated	ADJ
cana-934	88	11	vortex	vortex	NOUN
cana-934	88	12	dynamics	dynamic	NOUN
cana-934	88	13	offer	offer	VERB
cana-934	88	14	a	a	DET
cana-934	88	15	rich	rich	ADJ
cana-934	88	16	framework	framework	NOUN
cana-934	88	17	for	for	ADP
cana-934	88	18	quantum	quantum	ADJ
cana-934	88	19	simulations	simulation	NOUN
cana-934	88	20	.	.	PUNCT
cana-934	89	1	the	the	DET
cana-934	89	2	complex	complex	ADJ
cana-934	89	3	behavior	behavior	NOUN
cana-934	89	4	of	of	ADP
cana-934	89	5	vortices	vortex	NOUN
cana-934	89	6	in	in	ADP
cana-934	89	7	turbulent	turbulent	ADJ
cana-934	89	8	quantum	quantum	NOUN
cana-934	89	9	fluids	fluid	NOUN
cana-934	89	10	can	can	AUX
cana-934	89	11	be	be	AUX
cana-934	89	12	analogous	analogous	ADJ
cana-934	89	13	to	to	ADP
cana-934	89	14	various	various	ADJ
cana-934	89	15	phenomena	phenomenon	NOUN
cana-934	89	16	in	in	ADP
cana-934	89	17	condensed	condense	VERB
cana-934	89	18	matter	matter	NOUN
cana-934	89	19	physics	physics	NOUN
cana-934	89	20	,	,	PUNCT
cana-934	89	21	high	high	ADJ
cana-934	89	22	-	-	PUNCT
cana-934	89	23	energy	energy	NOUN
cana-934	89	24	physics	physics	NOUN
cana-934	89	25	,	,	PUNCT
cana-934	89	26	and	and	CCONJ
cana-934	89	27	cosmology	cosmology	NOUN
cana-934	89	28	.	.	PUNCT
cana-934	90	1	by	by	ADP
cana-934	90	2	simulating	simulate	VERB
cana-934	90	3	quantum	quantum	ADJ
cana-934	90	4	turbulence	turbulence	NOUN
cana-934	90	5	within	within	ADP
cana-934	90	6	the	the	DET
cana-934	90	7	qnlse	qnlse	ADJ
cana-934	90	8	framework	framework	NOUN
cana-934	90	9	,	,	PUNCT
cana-934	90	10	researchers	researcher	NOUN
cana-934	90	11	can	can	AUX
cana-934	90	12	gain	gain	VERB
cana-934	90	13	insights	insight	NOUN
cana-934	90	14	into	into	ADP
cana-934	90	15	these	these	DET
cana-934	90	16	phenomena	phenomenon	NOUN
cana-934	90	17	at	at	ADP
cana-934	90	18	a	a	DET
cana-934	90	19	more	more	ADV
cana-934	90	20	accessible	accessible	ADJ
cana-934	90	21	and	and	CCONJ
cana-934	90	22	controllable	controllable	ADJ
cana-934	90	23	scale	scale	NOUN
cana-934	90	24	.	.	PUNCT
cana-934	91	1	additionally	additionally	ADV
cana-934	91	2	,	,	PUNCT
cana-934	91	3	understanding	understand	VERB
cana-934	91	4	energy	energy	NOUN
cana-934	91	5	transfer	transfer	NOUN
cana-934	91	6	and	and	CCONJ
cana-934	91	7	dissipation	dissipation	NOUN
cana-934	91	8	in	in	ADP
cana-934	91	9	quantum	quantum	ADJ
cana-934	91	10	turbulent	turbulent	ADJ
cana-934	91	11	systems	system	NOUN
cana-934	91	12	could	could	AUX
cana-934	91	13	inform	inform	VERB
cana-934	91	14	the	the	DET
cana-934	91	15	design	design	NOUN
cana-934	91	16	of	of	ADP
cana-934	91	17	more	more	ADV
cana-934	91	18	efficient	efficient	ADJ
cana-934	91	19	quantum	quantum	NOUN
cana-934	91	20	devices	device	NOUN
cana-934	91	21	,	,	PUNCT
cana-934	91	22	where	where	SCONJ
cana-934	91	23	energy	energy	NOUN
cana-934	91	24	management	management	NOUN
cana-934	91	25	is	be	AUX
cana-934	91	26	crucial	crucial	ADJ
cana-934	91	27	for	for	ADP
cana-934	91	28	operation	operation	NOUN
cana-934	91	29	at	at	ADP
cana-934	91	30	quantum	quantum	ADJ
cana-934	91	31	limits	limit	NOUN
cana-934	91	32	.	.	PUNCT
cana-934	92	1	in	in	ADP
cana-934	92	2	conclusion	conclusion	NOUN
cana-934	92	3	,	,	PUNCT
cana-934	92	4	the	the	DET
cana-934	92	5	insights	insight	NOUN
cana-934	92	6	gleaned	glean	VERB
cana-934	92	7	from	from	ADP
cana-934	92	8	our	our	PRON
cana-934	92	9	study	study	NOUN
cana-934	92	10	of	of	ADP
cana-934	92	11	the	the	DET
cana-934	92	12	qnlse	qnlse	NOUN
cana-934	92	13	significantly	significantly	ADV
cana-934	92	14	contribute	contribute	VERB
cana-934	92	15	to	to	ADP
cana-934	92	16	the	the	DET
cana-934	92	17	foundational	foundational	ADJ
cana-934	92	18	knowledge	knowledge	NOUN
cana-934	92	19	necessary	necessary	ADJ
cana-934	92	20	for	for	ADP
cana-934	92	21	advancing	advance	VERB
cana-934	92	22	quantum	quantum	NOUN
cana-934	92	23	computing	computing	NOUN
cana-934	92	24	and	and	CCONJ
cana-934	92	25	simulation	simulation	NOUN
cana-934	92	26	.	.	PUNCT
cana-934	93	1	by	by	ADP
cana-934	93	2	harnessing	harness	VERB
cana-934	93	3	the	the	DET
cana-934	93	4	unique	unique	ADJ
cana-934	93	5	dynamics	dynamic	NOUN
cana-934	93	6	of	of	ADP
cana-934	93	7	quantum	quantum	NOUN
cana-934	93	8	chaos	chaos	NOUN
cana-934	93	9	,	,	PUNCT
cana-934	93	10	soliton	soliton	NOUN
cana-934	93	11	stability	stability	NOUN
cana-934	93	12	,	,	PUNCT
cana-934	93	13	and	and	CCONJ
cana-934	93	14	turbulence	turbulence	NOUN
cana-934	93	15	,	,	PUNCT
cana-934	93	16	we	we	PRON
cana-934	93	17	can	can	AUX
cana-934	93	18	develop	develop	VERB
cana-934	93	19	novel	novel	ADJ
cana-934	93	20	quantum	quantum	NOUN
cana-934	93	21	technologies	technology	NOUN
cana-934	93	22	with	with	ADP
cana-934	93	23	enhanced	enhanced	ADJ
cana-934	93	24	capabilities	capability	NOUN
cana-934	93	25	and	and	CCONJ
cana-934	93	26	performance	performance	NOUN
cana-934	93	27	,	,	PUNCT
cana-934	93	28	marking	mark	VERB
cana-934	93	29	a	a	DET
cana-934	93	30	significant	significant	ADJ
cana-934	93	31	step	step	NOUN
cana-934	93	32	forward	forward	ADV
cana-934	93	33	in	in	ADP
cana-934	93	34	the	the	DET
cana-934	93	35	realization	realization	NOUN
cana-934	93	36	of	of	ADP
cana-934	93	37	practical	practical	ADJ
cana-934	93	38	quantum	quantum	NOUN
cana-934	93	39	computing	computing	NOUN
cana-934	93	40	and	and	CCONJ
cana-934	93	41	communication	communication	NOUN
cana-934	93	42	systems	system	NOUN
cana-934	93	43	.	.	PUNCT
cana-934	94	1	v.	v.	ADP
cana-934	94	2	conclusion	conclusion	NOUN
cana-934	94	3	our	our	PRON
cana-934	94	4	comprehensive	comprehensive	ADJ
cana-934	94	5	study	study	NOUN
cana-934	94	6	of	of	ADP
cana-934	94	7	the	the	DET
cana-934	94	8	quantum	quantum	NOUN
cana-934	94	9	noise	noise	NOUN
cana-934	94	10	-	-	PUNCT
cana-934	94	11	extended	extend	VERB
cana-934	94	12	nonlinear	nonlinear	ADJ
cana-934	94	13	schrödinger	schrödinger	ADJ
cana-934	94	14	equation	equation	NOUN
cana-934	94	15	(	(	PUNCT
cana-934	94	16	qnlse	qnlse	PROPN
cana-934	94	17	)	)	PUNCT
cana-934	94	18	has	have	AUX
cana-934	94	19	unveiled	unveil	VERB
cana-934	94	20	pivotal	pivotal	ADJ
cana-934	94	21	insights	insight	NOUN
cana-934	94	22	into	into	ADP
cana-934	94	23	the	the	DET
cana-934	94	24	dynamics	dynamic	NOUN
cana-934	94	25	of	of	ADP
cana-934	94	26	quantum	quantum	NOUN
cana-934	94	27	systems	system	NOUN
cana-934	94	28	,	,	PUNCT
cana-934	94	29	emphasizing	emphasize	VERB
cana-934	94	30	the	the	DET
cana-934	94	31	phenomena	phenomenon	NOUN
cana-934	94	32	of	of	ADP
cana-934	94	33	quantum	quantum	NOUN
cana-934	94	34	chaos	chaos	NOUN
cana-934	94	35	,	,	PUNCT
cana-934	94	36	soliton	soliton	NOUN
cana-934	94	37	behavior	behavior	NOUN
cana-934	94	38	,	,	PUNCT
cana-934	94	39	and	and	CCONJ
cana-934	94	40	quantum	quantum	ADJ
cana-934	94	41	turbulence	turbulence	NOUN
cana-934	94	42	.	.	PUNCT
cana-934	95	1	these	these	DET
cana-934	95	2	findings	finding	NOUN
cana-934	95	3	elucidate	elucidate	VERB
cana-934	95	4	the	the	DET
cana-934	95	5	intricate	intricate	ADJ
cana-934	95	6	balance	balance	NOUN
cana-934	95	7	between	between	ADP
cana-934	95	8	nonlinearity	nonlinearity	NOUN
cana-934	95	9	,	,	PUNCT
cana-934	95	10	dispersion	dispersion	NOUN
cana-934	95	11	,	,	PUNCT
cana-934	95	12	and	and	CCONJ
cana-934	95	13	quantum	quantum	NOUN
cana-934	95	14	noise	noise	NOUN
cana-934	95	15	,	,	PUNCT
cana-934	95	16	providing	provide	VERB
cana-934	95	17	a	a	DET
cana-934	95	18	deeper	deep	ADJ
cana-934	95	19	understanding	understanding	NOUN
cana-934	95	20	of	of	ADP
cana-934	95	21	the	the	DET
cana-934	95	22	complex	complex	ADJ
cana-934	95	23	behaviors	behavior	NOUN
cana-934	95	24	characteristic	characteristic	ADJ
cana-934	95	25	of	of	ADP
cana-934	95	26	quantum	quantum	NOUN
cana-934	95	27	systems	system	NOUN
cana-934	95	28	.	.	PUNCT
cana-934	96	1	communications	communication	NOUN
cana-934	96	2	on	on	ADP
cana-934	96	3	applied	apply	VERB
cana-934	96	4	nonlinear	nonlinear	ADJ
cana-934	96	5	analysis	analysis	NOUN
cana-934	96	6	issn	issn	NOUN
cana-934	96	7	:	:	PUNCT
cana-934	96	8	1074	1074	NUM
cana-934	96	9	-	-	PUNCT
cana-934	96	10	133x	133x	NUM
cana-934	96	11	vol	vol	NOUN
cana-934	96	12	31	31	NUM
cana-934	96	13	no	no	NOUN
cana-934	96	14	.	.	PUNCT
cana-934	97	1	4s	4s	NUM
cana-934	97	2	(	(	PUNCT
cana-934	97	3	2024	2024	NUM
cana-934	97	4	)	)	PUNCT
cana-934	97	5	416	416	NUM
cana-934	97	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-934	97	7	key	key	ADJ
cana-934	97	8	findings	finding	NOUN
cana-934	97	9	:	:	PUNCT
cana-934	97	10	•	•	NUM
cana-934	97	11	quantum	quantum	NOUN
cana-934	97	12	chaos	chaos	NOUN
cana-934	97	13	:	:	PUNCT
cana-934	97	14	we	we	PRON
cana-934	97	15	identified	identify	VERB
cana-934	97	16	conditions	condition	NOUN
cana-934	97	17	under	under	ADP
cana-934	97	18	which	which	PRON
cana-934	97	19	quantum	quantum	NOUN
cana-934	97	20	systems	system	NOUN
cana-934	97	21	transition	transition	NOUN
cana-934	97	22	into	into	ADP
cana-934	97	23	chaotic	chaotic	ADJ
cana-934	97	24	dynamics	dynamic	NOUN
cana-934	97	25	,	,	PUNCT
cana-934	97	26	driven	drive	VERB
cana-934	97	27	by	by	ADP
cana-934	97	28	the	the	DET
cana-934	97	29	interplay	interplay	NOUN
cana-934	97	30	between	between	ADP
cana-934	97	31	quantum	quantum	NOUN
cana-934	97	32	noise	noise	NOUN
cana-934	97	33	and	and	CCONJ
cana-934	97	34	nonlinearity	nonlinearity	NOUN
cana-934	97	35	.	.	PUNCT
cana-934	98	1	this	this	DET
cana-934	98	2	revelation	revelation	NOUN
cana-934	98	3	has	have	VERB
cana-934	98	4	profound	profound	ADJ
cana-934	98	5	implications	implication	NOUN
cana-934	98	6	for	for	ADP
cana-934	98	7	quantum	quantum	NOUN
cana-934	98	8	computing	computing	NOUN
cana-934	98	9	,	,	PUNCT
cana-934	98	10	suggesting	suggest	VERB
cana-934	98	11	both	both	CCONJ
cana-934	98	12	challenges	challenge	NOUN
cana-934	98	13	and	and	CCONJ
cana-934	98	14	opportunities	opportunity	NOUN
cana-934	98	15	in	in	ADP
cana-934	98	16	harnessing	harness	VERB
cana-934	98	17	chaos	chaos	NOUN
cana-934	98	18	for	for	ADP
cana-934	98	19	enhancing	enhance	VERB
cana-934	98	20	computational	computational	ADJ
cana-934	98	21	algorithms	algorithm	NOUN
cana-934	98	22	and	and	CCONJ
cana-934	98	23	securing	secure	VERB
cana-934	98	24	quantum	quantum	ADJ
cana-934	98	25	communications	communication	NOUN
cana-934	98	26	.	.	PUNCT
cana-934	99	1	•	•	NUM
cana-934	99	2	soliton	soliton	NOUN
cana-934	99	3	dynamics	dynamic	NOUN
cana-934	99	4	:	:	PUNCT
cana-934	99	5	our	our	PRON
cana-934	99	6	research	research	NOUN
cana-934	99	7	demonstrated	demonstrate	VERB
cana-934	99	8	the	the	DET
cana-934	99	9	remarkable	remarkable	ADJ
cana-934	99	10	stability	stability	NOUN
cana-934	99	11	of	of	ADP
cana-934	99	12	solitons	soliton	NOUN
cana-934	99	13	within	within	ADP
cana-934	99	14	the	the	DET
cana-934	99	15	qnlse	qnlse	ADJ
cana-934	99	16	framework	framework	NOUN
cana-934	99	17	,	,	PUNCT
cana-934	99	18	even	even	ADV
cana-934	99	19	amidst	amidst	ADP
cana-934	99	20	quantum	quantum	ADJ
cana-934	99	21	noise	noise	NOUN
cana-934	99	22	and	and	CCONJ
cana-934	99	23	interactions	interaction	NOUN
cana-934	99	24	.	.	PUNCT
cana-934	100	1	this	this	DET
cana-934	100	2	stability	stability	NOUN
cana-934	100	3	offers	offer	VERB
cana-934	100	4	promising	promise	VERB
cana-934	100	5	avenues	avenue	NOUN
cana-934	100	6	for	for	ADP
cana-934	100	7	utilizing	utilize	VERB
cana-934	100	8	solitons	soliton	NOUN
cana-934	100	9	in	in	ADP
cana-934	100	10	quantum	quantum	ADJ
cana-934	100	11	information	information	NOUN
cana-934	100	12	processing	processing	NOUN
cana-934	100	13	and	and	CCONJ
cana-934	100	14	long	long	ADJ
cana-934	100	15	-	-	PUNCT
cana-934	100	16	distance	distance	NOUN
cana-934	100	17	communication	communication	NOUN
cana-934	100	18	.	.	PUNCT
cana-934	101	1	•	•	NUM
cana-934	101	2	quantum	quantum	ADJ
cana-934	101	3	turbulence	turbulence	NOUN
cana-934	101	4	:	:	PUNCT
cana-934	101	5	the	the	DET
cana-934	101	6	emergence	emergence	NOUN
cana-934	101	7	of	of	ADP
cana-934	101	8	quantum	quantum	ADJ
cana-934	101	9	turbulence	turbulence	NOUN
cana-934	101	10	and	and	CCONJ
cana-934	101	11	vortex	vortex	NOUN
cana-934	101	12	dynamics	dynamic	NOUN
cana-934	101	13	presents	present	VERB
cana-934	101	14	a	a	DET
cana-934	101	15	novel	novel	ADJ
cana-934	101	16	perspective	perspective	NOUN
cana-934	101	17	on	on	ADP
cana-934	101	18	energy	energy	NOUN
cana-934	101	19	transfer	transfer	NOUN
cana-934	101	20	and	and	CCONJ
cana-934	101	21	dissipation	dissipation	NOUN
cana-934	101	22	in	in	ADP
cana-934	101	23	quantum	quantum	NOUN
cana-934	101	24	fluids	fluid	NOUN
cana-934	101	25	.	.	PUNCT
cana-934	102	1	this	this	DET
cana-934	102	2	phenomenon	phenomenon	NOUN
cana-934	102	3	could	could	AUX
cana-934	102	4	serve	serve	VERB
cana-934	102	5	as	as	ADP
cana-934	102	6	a	a	DET
cana-934	102	7	valuable	valuable	ADJ
cana-934	102	8	model	model	NOUN
cana-934	102	9	for	for	ADP
cana-934	102	10	exploring	explore	VERB
cana-934	102	11	analogous	analogous	ADJ
cana-934	102	12	behaviors	behavior	NOUN
cana-934	102	13	in	in	ADP
cana-934	102	14	diverse	diverse	ADJ
cana-934	102	15	physical	physical	ADJ
cana-934	102	16	systems	system	NOUN
cana-934	102	17	,	,	PUNCT
cana-934	102	18	from	from	ADP
cana-934	102	19	condensed	condense	VERB
cana-934	102	20	matter	matter	NOUN
cana-934	102	21	to	to	ADP
cana-934	102	22	cosmological	cosmological	ADJ
cana-934	102	23	scales	scale	NOUN
cana-934	102	24	.	.	PUNCT
cana-934	103	1	future	future	ADJ
cana-934	103	2	directions	direction	NOUN
cana-934	103	3	:	:	PUNCT
cana-934	103	4	•	•	NUM
cana-934	103	5	control	control	NOUN
cana-934	103	6	of	of	ADP
cana-934	103	7	quantum	quantum	NOUN
cana-934	103	8	chaos	chaos	NOUN
cana-934	103	9	:	:	PUNCT
cana-934	103	10	further	further	ADJ
cana-934	103	11	research	research	NOUN
cana-934	103	12	should	should	AUX
cana-934	103	13	aim	aim	VERB
cana-934	103	14	at	at	ADP
cana-934	103	15	developing	develop	VERB
cana-934	103	16	techniques	technique	NOUN
cana-934	103	17	to	to	PART
cana-934	103	18	control	control	VERB
cana-934	103	19	and	and	CCONJ
cana-934	103	20	harness	harness	ADJ
cana-934	103	21	quantum	quantum	NOUN
cana-934	103	22	chaos	chaos	NOUN
cana-934	103	23	,	,	PUNCT
cana-934	103	24	potentially	potentially	ADV
cana-934	103	25	leading	lead	VERB
cana-934	103	26	to	to	ADP
cana-934	103	27	innovative	innovative	ADJ
cana-934	103	28	quantum	quantum	ADJ
cana-934	103	29	cryptographic	cryptographic	ADJ
cana-934	103	30	methods	method	NOUN
cana-934	103	31	and	and	CCONJ
cana-934	103	32	more	more	ADV
cana-934	103	33	efficient	efficient	ADJ
cana-934	103	34	quantum	quantum	ADJ
cana-934	103	35	algorithms	algorithm	NOUN
cana-934	103	36	.	.	PUNCT
cana-934	104	1	•	•	NUM
cana-934	104	2	soliton	soliton	NOUN
cana-934	104	3	-	-	PUNCT
cana-934	104	4	based	base	VERB
cana-934	104	5	quantum	quantum	NOUN
cana-934	104	6	technologies	technology	NOUN
cana-934	104	7	:	:	PUNCT
cana-934	104	8	exploring	explore	VERB
cana-934	104	9	the	the	DET
cana-934	104	10	potential	potential	NOUN
cana-934	104	11	of	of	ADP
cana-934	104	12	solitons	soliton	NOUN
cana-934	104	13	for	for	ADP
cana-934	104	14	quantum	quantum	NOUN
cana-934	104	15	computing	computing	NOUN
cana-934	104	16	and	and	CCONJ
cana-934	104	17	communication	communication	NOUN
cana-934	104	18	requires	require	VERB
cana-934	104	19	deeper	deep	ADJ
cana-934	104	20	investigation	investigation	NOUN
cana-934	104	21	into	into	ADP
cana-934	104	22	their	their	PRON
cana-934	104	23	interaction	interaction	NOUN
cana-934	104	24	mechanisms	mechanism	NOUN
cana-934	104	25	and	and	CCONJ
cana-934	104	26	stability	stability	NOUN
cana-934	104	27	under	under	ADP
cana-934	104	28	various	various	ADJ
cana-934	104	29	conditions	condition	NOUN
cana-934	104	30	.	.	PUNCT
cana-934	105	1	future	future	ADJ
cana-934	105	2	studies	study	NOUN
cana-934	105	3	could	could	AUX
cana-934	105	4	focus	focus	VERB
cana-934	105	5	on	on	ADP
cana-934	105	6	leveraging	leverage	VERB
cana-934	105	7	solitons	soliton	NOUN
cana-934	105	8	for	for	ADP
cana-934	105	9	quantum	quantum	ADJ
cana-934	105	10	logic	logic	NOUN
cana-934	105	11	operations	operation	NOUN
cana-934	105	12	and	and	CCONJ
cana-934	105	13	as	as	ADP
cana-934	105	14	carriers	carrier	NOUN
cana-934	105	15	of	of	ADP
cana-934	105	16	quantum	quantum	ADJ
cana-934	105	17	information	information	NOUN
cana-934	105	18	across	across	ADP
cana-934	105	19	quantum	quantum	NOUN
cana-934	105	20	networks	network	NOUN
cana-934	105	21	.	.	PUNCT
cana-934	106	1	•	•	NUM
cana-934	106	2	simulation	simulation	NOUN
cana-934	106	3	of	of	ADP
cana-934	106	4	quantum	quantum	ADJ
cana-934	106	5	turbulence	turbulence	NOUN
cana-934	106	6	:	:	PUNCT
cana-934	106	7	advancing	advance	VERB
cana-934	106	8	the	the	DET
cana-934	106	9	simulation	simulation	NOUN
cana-934	106	10	techniques	technique	NOUN
cana-934	106	11	for	for	ADP
cana-934	106	12	quantum	quantum	ADJ
cana-934	106	13	turbulence	turbulence	NOUN
cana-934	106	14	can	can	AUX
cana-934	106	15	unlock	unlock	VERB
cana-934	106	16	new	new	ADJ
cana-934	106	17	insights	insight	NOUN
cana-934	106	18	into	into	ADP
cana-934	106	19	the	the	DET
cana-934	106	20	fundamental	fundamental	ADJ
cana-934	106	21	principles	principle	NOUN
cana-934	106	22	governing	govern	VERB
cana-934	106	23	turbulent	turbulent	ADJ
cana-934	106	24	quantum	quantum	NOUN
cana-934	106	25	fluids	fluid	NOUN
cana-934	106	26	.	.	PUNCT
cana-934	107	1	this	this	PRON
cana-934	107	2	could	could	AUX
cana-934	107	3	pave	pave	VERB
cana-934	107	4	the	the	DET
cana-934	107	5	way	way	NOUN
cana-934	107	6	for	for	ADP
cana-934	107	7	simulating	simulate	VERB
cana-934	107	8	complex	complex	ADJ
cana-934	107	9	phenomena	phenomenon	NOUN
cana-934	107	10	in	in	ADP
cana-934	107	11	a	a	DET
cana-934	107	12	controlled	control	VERB
cana-934	107	13	quantum	quantum	NOUN
cana-934	107	14	environment	environment	NOUN
cana-934	107	15	,	,	PUNCT
cana-934	107	16	offering	offer	VERB
cana-934	107	17	a	a	DET
cana-934	107	18	deeper	deep	ADJ
cana-934	107	19	understanding	understanding	NOUN
cana-934	107	20	of	of	ADP
cana-934	107	21	turbulence	turbulence	NOUN
cana-934	107	22	in	in	ADP
cana-934	107	23	nature	nature	NOUN
cana-934	107	24	and	and	CCONJ
cana-934	107	25	its	its	PRON
cana-934	107	26	applications	application	NOUN
cana-934	107	27	in	in	ADP
cana-934	107	28	technology	technology	NOUN
cana-934	107	29	.	.	PUNCT
cana-934	108	1	in	in	ADP
cana-934	108	2	conclusion	conclusion	NOUN
cana-934	108	3	,	,	PUNCT
cana-934	108	4	our	our	PRON
cana-934	108	5	study	study	NOUN
cana-934	108	6	contributes	contribute	VERB
cana-934	108	7	significantly	significantly	ADV
cana-934	108	8	to	to	ADP
cana-934	108	9	the	the	DET
cana-934	108	10	field	field	NOUN
cana-934	108	11	of	of	ADP
cana-934	108	12	quantum	quantum	NOUN
cana-934	108	13	physics	physics	NOUN
cana-934	108	14	,	,	PUNCT
cana-934	108	15	offering	offer	VERB
cana-934	108	16	new	new	ADJ
cana-934	108	17	perspectives	perspective	NOUN
cana-934	108	18	on	on	ADP
cana-934	108	19	the	the	DET
cana-934	108	20	dynamics	dynamic	NOUN
cana-934	108	21	governed	govern	VERB
cana-934	108	22	by	by	ADP
cana-934	108	23	the	the	DET
cana-934	108	24	qnlse	qnlse	PROPN
cana-934	108	25	.	.	PUNCT
cana-934	109	1	the	the	DET
cana-934	109	2	implications	implication	NOUN
cana-934	109	3	of	of	ADP
cana-934	109	4	our	our	PRON
cana-934	109	5	findings	finding	NOUN
cana-934	109	6	extend	extend	VERB
cana-934	109	7	beyond	beyond	ADP
cana-934	109	8	theoretical	theoretical	ADJ
cana-934	109	9	interest	interest	NOUN
cana-934	109	10	,	,	PUNCT
cana-934	109	11	touching	touch	VERB
cana-934	109	12	upon	upon	SCONJ
cana-934	109	13	practical	practical	ADJ
cana-934	109	14	applications	application	NOUN
cana-934	109	15	in	in	ADP
cana-934	109	16	quantum	quantum	ADJ
cana-934	109	17	technology	technology	NOUN
cana-934	109	18	.	.	PUNCT
cana-934	110	1	as	as	SCONJ
cana-934	110	2	we	we	PRON
cana-934	110	3	move	move	VERB
cana-934	110	4	forward	forward	ADV
cana-934	110	5	,	,	PUNCT
cana-934	110	6	it	it	PRON
cana-934	110	7	is	be	AUX
cana-934	110	8	imperative	imperative	ADJ
cana-934	110	9	to	to	PART
cana-934	110	10	continue	continue	VERB
cana-934	110	11	exploring	explore	VERB
cana-934	110	12	these	these	DET
cana-934	110	13	phenomena	phenomenon	NOUN
cana-934	110	14	,	,	PUNCT
cana-934	110	15	delving	delve	VERB
cana-934	110	16	deeper	deeply	ADV
cana-934	110	17	into	into	ADP
cana-934	110	18	their	their	PRON
cana-934	110	19	theoretical	theoretical	ADJ
cana-934	110	20	foundations	foundation	NOUN
cana-934	110	21	and	and	CCONJ
cana-934	110	22	practical	practical	ADJ
cana-934	110	23	applications	application	NOUN
cana-934	110	24	.	.	PUNCT
cana-934	111	1	through	through	ADP
cana-934	111	2	sustained	sustained	ADJ
cana-934	111	3	research	research	NOUN
cana-934	111	4	and	and	CCONJ
cana-934	111	5	exploration	exploration	NOUN
cana-934	111	6	,	,	PUNCT
cana-934	111	7	we	we	PRON
cana-934	111	8	can	can	AUX
cana-934	111	9	harness	harness	VERB
cana-934	111	10	the	the	DET
cana-934	111	11	full	full	ADJ
cana-934	111	12	potential	potential	NOUN
cana-934	111	13	of	of	ADP
cana-934	111	14	quantum	quantum	NOUN
cana-934	111	15	systems	system	NOUN
cana-934	111	16	,	,	PUNCT
cana-934	111	17	paving	pave	VERB
cana-934	111	18	the	the	DET
cana-934	111	19	way	way	NOUN
cana-934	111	20	for	for	ADP
cana-934	111	21	groundbreaking	groundbreake	VERB
cana-934	111	22	advancements	advancement	NOUN
cana-934	111	23	in	in	ADP
cana-934	111	24	quantum	quantum	NOUN
cana-934	111	25	computing	computing	NOUN
cana-934	111	26	and	and	CCONJ
cana-934	111	27	beyond	beyond	ADP
cana-934	111	28	.	.	PUNCT
cana-934	112	1	references	reference	NOUN
cana-934	112	2	[	[	X
cana-934	112	3	1	1	NUM
cana-934	112	4	]	]	PUNCT
cana-934	112	5	ablowitz	ablowitz	NOUN
cana-934	112	6	,	,	PUNCT
cana-934	112	7	m.	m.	NOUN
cana-934	112	8	j.	j.	PROPN
cana-934	112	9	,	,	PUNCT
cana-934	112	10	&	&	CCONJ
cana-934	112	11	segur	segur	PROPN
cana-934	112	12	,	,	PUNCT
cana-934	112	13	h.	h.	PROPN
cana-934	112	14	(	(	PUNCT
cana-934	112	15	1981	1981	NUM
cana-934	112	16	)	)	PUNCT
cana-934	112	17	.	.	PUNCT
cana-934	113	1	solitons	soliton	NOUN
cana-934	113	2	and	and	CCONJ
cana-934	113	3	the	the	DET
cana-934	113	4	inverse	inverse	NOUN
cana-934	113	5	scattering	scattering	NOUN
cana-934	113	6	transform	transform	NOUN
cana-934	113	7	.	.	PUNCT
cana-934	114	1	siam	siam	NOUN
cana-934	114	2	.	.	PUNCT
cana-934	115	1	[	[	X
cana-934	115	2	2	2	NUM
cana-934	115	3	]	]	PUNCT
cana-934	115	4	agrawal	agrawal	PROPN
cana-934	115	5	,	,	PUNCT
cana-934	115	6	g.	g.	PROPN
cana-934	115	7	p.	p.	PROPN
cana-934	115	8	(	(	PUNCT
cana-934	115	9	2013	2013	NUM
cana-934	115	10	)	)	PUNCT
cana-934	115	11	.	.	PUNCT
cana-934	116	1	nonlinear	nonlinear	ADJ
cana-934	116	2	fiber	fiber	NOUN
cana-934	116	3	optics	optic	NOUN
cana-934	116	4	.	.	PUNCT
cana-934	117	1	academic	academic	ADJ
cana-934	117	2	press	press	NOUN
cana-934	117	3	.	.	PUNCT
cana-934	118	1	[	[	X
cana-934	118	2	3	3	X
cana-934	118	3	]	]	X
cana-934	118	4	dalfovo	dalfovo	PROPN
cana-934	118	5	,	,	PUNCT
cana-934	118	6	f.	f.	PROPN
cana-934	118	7	,	,	PUNCT
cana-934	118	8	giorgini	giorgini	PROPN
cana-934	118	9	,	,	PUNCT
cana-934	118	10	s.	s.	PROPN
cana-934	118	11	,	,	PUNCT
cana-934	118	12	pitaevskii	pitaevskii	PROPN
cana-934	118	13	,	,	PUNCT
cana-934	118	14	l.	l.	PROPN
cana-934	118	15	p.	p.	PROPN
cana-934	118	16	,	,	PUNCT
cana-934	118	17	&	&	CCONJ
cana-934	118	18	stringari	stringari	PROPN
cana-934	118	19	,	,	PUNCT
cana-934	118	20	s.	s.	PROPN
cana-934	118	21	(	(	PUNCT
cana-934	118	22	1999	1999	NUM
cana-934	118	23	)	)	PUNCT
cana-934	118	24	.	.	PUNCT
cana-934	119	1	theory	theory	NOUN
cana-934	119	2	of	of	ADP
cana-934	119	3	bose	bose	NOUN
cana-934	119	4	-	-	PUNCT
cana-934	119	5	einstein	einstein	NOUN
cana-934	119	6	condensation	condensation	NOUN
cana-934	119	7	in	in	ADP
cana-934	119	8	trapped	trap	VERB
cana-934	119	9	gases	gas	NOUN
cana-934	119	10	.	.	PUNCT
cana-934	120	1	reviews	review	NOUN
cana-934	120	2	of	of	ADP
cana-934	120	3	modern	modern	ADJ
cana-934	120	4	physics	physic	NOUN
cana-934	120	5	,	,	PUNCT
cana-934	120	6	71(3	71(3	NUM
cana-934	120	7	)	)	PUNCT
cana-934	120	8	,	,	PUNCT
cana-934	120	9	463	463	NUM
cana-934	120	10	.	.	PUNCT
cana-934	121	1	[	[	X
cana-934	121	2	4	4	NUM
cana-934	121	3	]	]	X
cana-934	121	4	gardiner	gardiner	NOUN
cana-934	121	5	,	,	PUNCT
cana-934	121	6	c.	c.	PROPN
cana-934	121	7	w.	w.	PROPN
cana-934	121	8	,	,	PUNCT
cana-934	121	9	&	&	CCONJ
cana-934	121	10	zoller	zoller	PROPN
cana-934	121	11	,	,	PUNCT
cana-934	121	12	p.	p.	NOUN
cana-934	121	13	(	(	PUNCT
cana-934	121	14	2004	2004	NUM
cana-934	121	15	)	)	PUNCT
cana-934	121	16	.	.	PUNCT
cana-934	122	1	quantum	quantum	NOUN
cana-934	122	2	noise	noise	NOUN
cana-934	122	3	.	.	PUNCT
cana-934	123	1	springer	springer	NOUN
cana-934	123	2	-	-	PUNCT
cana-934	123	3	verlag	verlag	PROPN
cana-934	123	4	.	.	PUNCT
cana-934	124	1	[	[	X
cana-934	124	2	5	5	NUM
cana-934	124	3	]	]	PUNCT
cana-934	124	4	hasegawa	hasegawa	PROPN
cana-934	124	5	,	,	PUNCT
cana-934	124	6	a.	a.	PROPN
cana-934	124	7	,	,	PUNCT
cana-934	124	8	&	&	CCONJ
cana-934	124	9	kodama	kodama	PROPN
cana-934	124	10	,	,	PUNCT
cana-934	124	11	y.	y.	PROPN
cana-934	124	12	(	(	PUNCT
cana-934	124	13	1995	1995	NUM
cana-934	124	14	)	)	PUNCT
cana-934	124	15	.	.	PUNCT
cana-934	125	1	solitons	soliton	NOUN
cana-934	125	2	in	in	ADP
cana-934	125	3	optical	optical	ADJ
cana-934	125	4	communications	communication	NOUN
cana-934	125	5	.	.	PUNCT
cana-934	126	1	clarendon	clarendon	PROPN
cana-934	126	2	press	press	PROPN
cana-934	126	3	.	.	PUNCT
cana-934	127	1	communications	communication	NOUN
cana-934	127	2	on	on	ADP
cana-934	127	3	applied	apply	VERB
cana-934	127	4	nonlinear	nonlinear	ADJ
cana-934	127	5	analysis	analysis	NOUN
cana-934	127	6	issn	issn	NOUN
cana-934	127	7	:	:	PUNCT
cana-934	127	8	1074	1074	NUM
cana-934	127	9	-	-	PUNCT
cana-934	127	10	133x	133x	NUM
cana-934	127	11	vol	vol	NOUN
cana-934	127	12	31	31	NUM
cana-934	127	13	no	no	NOUN
cana-934	127	14	.	.	PUNCT
cana-934	128	1	4s	4s	NUM
cana-934	128	2	(	(	PUNCT
cana-934	128	3	2024	2024	NUM
cana-934	128	4	)	)	PUNCT
cana-934	128	5	417	417	NUM
cana-934	128	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-934	129	1	[	[	X
cana-934	129	2	6	6	NUM
cana-934	129	3	]	]	PUNCT
cana-934	129	4	kevrekidis	kevrekidi	NOUN
cana-934	129	5	,	,	PUNCT
cana-934	129	6	p.	p.	PROPN
cana-934	129	7	g.	g.	PROPN
cana-934	129	8	,	,	PUNCT
cana-934	129	9	frantzeskakis	frantzeskakis	PROPN
cana-934	129	10	,	,	PUNCT
cana-934	129	11	d.	d.	PROPN
cana-934	129	12	j.	j.	PROPN
cana-934	129	13	,	,	PUNCT
cana-934	129	14	&	&	CCONJ
cana-934	129	15	carretero	carretero	NOUN
cana-934	129	16	-	-	PUNCT
cana-934	129	17	gonzález	gonzález	PROPN
cana-934	129	18	,	,	PUNCT
cana-934	129	19	r.	r.	PROPN
cana-934	129	20	(	(	PUNCT
cana-934	129	21	eds	eds	PROPN
cana-934	129	22	.	.	PUNCT
cana-934	129	23	)	)	PUNCT
cana-934	129	24	.	.	PUNCT
cana-934	130	1	(	(	PUNCT
cana-934	130	2	2008	2008	NUM
cana-934	130	3	)	)	PUNCT
cana-934	130	4	.	.	PUNCT
cana-934	131	1	emergent	emergent	ADJ
cana-934	131	2	nonlinear	nonlinear	ADJ
cana-934	131	3	phenomena	phenomenon	NOUN
cana-934	131	4	in	in	ADP
cana-934	131	5	bose	bose	NOUN
cana-934	131	6	-	-	PUNCT
cana-934	131	7	einstein	einstein	NOUN
cana-934	131	8	condensates	condensate	NOUN
cana-934	131	9	:	:	PUNCT
cana-934	131	10	theory	theory	NOUN
cana-934	131	11	and	and	CCONJ
cana-934	131	12	experiment	experiment	NOUN
cana-934	131	13	.	.	PUNCT
cana-934	132	1	springer	springer	NOUN
cana-934	132	2	.	.	PUNCT
cana-934	133	1	[	[	X
cana-934	133	2	7	7	NUM
cana-934	133	3	]	]	PUNCT
cana-934	133	4	laskin	laskin	NOUN
cana-934	133	5	,	,	PUNCT
cana-934	133	6	n.	n.	NOUN
cana-934	133	7	(	(	PUNCT
cana-934	133	8	2000	2000	NUM
cana-934	133	9	)	)	PUNCT
cana-934	133	10	.	.	PUNCT
cana-934	134	1	fractional	fractional	ADJ
cana-934	134	2	quantum	quantum	ADJ
cana-934	134	3	mechanics	mechanic	NOUN
cana-934	134	4	and	and	CCONJ
cana-934	134	5	lévy	lévy	ADJ
cana-934	134	6	path	path	NOUN
cana-934	134	7	integrals	integral	NOUN
cana-934	134	8	.	.	PUNCT
cana-934	135	1	physics	physics	NOUN
cana-934	135	2	letters	letter	NOUN
cana-934	135	3	a	a	PRON
cana-934	135	4	,	,	PUNCT
cana-934	135	5	268(4	268(4	NUM
cana-934	135	6	-	-	SYM
cana-934	135	7	6	6	NUM
cana-934	135	8	)	)	PUNCT
cana-934	135	9	,	,	PUNCT
cana-934	135	10	298	298	NUM
cana-934	135	11	-	-	SYM
cana-934	135	12	305	305	NUM
cana-934	135	13	.	.	PUNCT
cana-934	136	1	[	[	X
cana-934	136	2	8	8	NUM
cana-934	136	3	]	]	X
cana-934	136	4	scott	scott	PROPN
cana-934	136	5	,	,	PUNCT
cana-934	136	6	a.	a.	PROPN
cana-934	136	7	c.	c.	PROPN
cana-934	136	8	(	(	PUNCT
cana-934	136	9	2003	2003	NUM
cana-934	136	10	)	)	PUNCT
cana-934	136	11	.	.	PUNCT
cana-934	137	1	nonlinear	nonlinear	ADJ
cana-934	137	2	science	science	NOUN
cana-934	137	3	:	:	PUNCT
cana-934	137	4	emergence	emergence	NOUN
cana-934	137	5	and	and	CCONJ
cana-934	137	6	dynamics	dynamic	NOUN
cana-934	137	7	of	of	ADP
cana-934	137	8	coherent	coherent	ADJ
cana-934	137	9	structures	structure	NOUN
cana-934	137	10	.	.	PUNCT
cana-934	138	1	oxford	oxford	PROPN
cana-934	138	2	university	university	PROPN
cana-934	138	3	press	press	NOUN
cana-934	138	4	.	.	PUNCT
cana-934	139	1	[	[	X
cana-934	139	2	9	9	NUM
cana-934	139	3	]	]	SYM
cana-934	139	4	sulem	sulem	NOUN
cana-934	139	5	,	,	PUNCT
cana-934	139	6	c.	c.	PROPN
cana-934	139	7	,	,	PUNCT
cana-934	139	8	&	&	CCONJ
cana-934	139	9	sulem	sulem	PROPN
cana-934	139	10	,	,	PUNCT
cana-934	139	11	p.	p.	PROPN
cana-934	139	12	l.	l.	PROPN
cana-934	139	13	(	(	PUNCT
cana-934	139	14	1999	1999	NUM
cana-934	139	15	)	)	PUNCT
cana-934	139	16	.	.	PUNCT
cana-934	140	1	the	the	DET
cana-934	140	2	nonlinear	nonlinear	ADJ
cana-934	140	3	schrödinger	schrödinger	ADJ
cana-934	140	4	equation	equation	NOUN
cana-934	140	5	:	:	PUNCT
cana-934	140	6	self	self	NOUN
cana-934	140	7	-	-	PUNCT
cana-934	140	8	focusing	focus	VERB
cana-934	140	9	and	and	CCONJ
cana-934	140	10	wave	wave	NOUN
cana-934	140	11	collapse	collapse	NOUN
cana-934	140	12	.	.	PUNCT
cana-934	141	1	springer	springer	NOUN
cana-934	141	2	-	-	PUNCT
cana-934	141	3	verlag	verlag	PROPN
cana-934	141	4	.	.	PUNCT
cana-934	142	1	[	[	X
cana-934	142	2	10	10	NUM
cana-934	142	3	]	]	X
cana-934	142	4	zakharov	zakharov	PROPN
cana-934	142	5	,	,	PUNCT
cana-934	142	6	v.	v.	PROPN
cana-934	142	7	e.	e.	PROPN
cana-934	142	8	,	,	PUNCT
cana-934	142	9	&	&	CCONJ
cana-934	142	10	shabat	shabat	PROPN
cana-934	142	11	,	,	PUNCT
cana-934	142	12	a.	a.	PROPN
cana-934	142	13	b.	b.	PROPN
cana-934	142	14	(	(	PUNCT
cana-934	142	15	1972	1972	NUM
cana-934	142	16	)	)	PUNCT
cana-934	142	17	.	.	PUNCT
cana-934	143	1	exact	exact	ADJ
cana-934	143	2	theory	theory	NOUN
cana-934	143	3	of	of	ADP
cana-934	143	4	two	two	NUM
cana-934	143	5	-	-	PUNCT
cana-934	143	6	dimensional	dimensional	ADJ
cana-934	143	7	self	self	NOUN
cana-934	143	8	-	-	PUNCT
cana-934	143	9	focusing	focus	VERB
cana-934	143	10	and	and	CCONJ
cana-934	143	11	one	one	NUM
cana-934	143	12	-	-	PUNCT
cana-934	143	13	dimensional	dimensional	ADJ
cana-934	143	14	selfmodulation	selfmodulation	NOUN
cana-934	143	15	of	of	ADP
cana-934	143	16	waves	wave	NOUN
cana-934	143	17	in	in	ADP
cana-934	143	18	nonlinear	nonlinear	ADJ
cana-934	143	19	media	medium	NOUN
cana-934	143	20	.	.	PUNCT
cana-934	144	1	soviet	soviet	ADJ
cana-934	144	2	physics	physics	PROPN
cana-934	144	3	jetp	jetp	PROPN
cana-934	144	4	,	,	PUNCT
cana-934	144	5	34(1	34(1	NUM
cana-934	144	6	)	)	PUNCT
cana-934	144	7	,	,	PUNCT
cana-934	144	8	62	62	NUM
cana-934	144	9	-	-	SYM
cana-934	144	10	69	69	NUM
cana-934	144	11	.	.	PUNCT