Infinite hierarchy of nonlinear Schrödinger equations and their solutions.

Ankiewicz, A; Kedziora, DJ; Chowdury, A; Bandelow, U; Akhmediev, N

Infinite hierarchy of nonlinear Schrödinger equations and their solutions.

Ankiewicz, A Kedziora, DJ Chowdury, A Bandelow, U Akhmediev, N

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Publisher:: AMER PHYSICAL SOC
Publication Type:: Journal Article
Citation:: Phys Rev E, 2016, 93, (1), pp. 012206
Issue Date:: 2016-01

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Field	Value	Language
dc.contributor.author	Ankiewicz, A
dc.contributor.author	Kedziora, DJ
dc.contributor.author	Chowdury, A
dc.contributor.author	Bandelow, U
dc.contributor.author	Akhmediev, N
dc.date.accessioned	2022-08-14T02:23:43Z
dc.date.available	2022-08-14T02:23:43Z
dc.date.issued	2016-01
dc.identifier.citation	Phys Rev E, 2016, 93, (1), pp. 012206
dc.identifier.issn	2470-0045
dc.identifier.issn	2470-0053
dc.identifier.uri	http://hdl.handle.net/10453/160116
dc.description.abstract	We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that "even- order" equations in the set affect phase and "stretching factors" in the solutions, while "odd-order" equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.
dc.format	Print-Electronic
dc.language	eng
dc.publisher	AMER PHYSICAL SOC
dc.relation.ispartof	Phys Rev E
dc.relation.isbasedon	10.1103/PhysRevE.93.012206
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	01 Mathematical Sciences, 02 Physical Sciences, 09 Engineering
dc.subject.classification	Fluids & Plasmas
dc.title	Infinite hierarchy of nonlinear Schrödinger equations and their solutions.
dc.type	Journal Article
utslib.citation.volume	93
utslib.location.activity	United States
utslib.for	01 Mathematical Sciences
utslib.for	02 Physical Sciences
utslib.for	09 Engineering
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - AAI - Advanced Analytics Institute Research Centre
utslib.copyright.status	closed_access	*
dc.date.updated	2022-08-14T02:23:42Z
pubs.issue	1
pubs.publication-status	Published
pubs.volume	93
utslib.citation.issue	1

Abstract:

We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that "even- order" equations in the set affect phase and "stretching factors" in the solutions, while "odd-order" equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.

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http://hdl.handle.net/10453/160116