Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms.

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

Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms.

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

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Publisher:: AMER PHYSICAL SOC
Publication Type:: Journal Article
Citation:: Phys Rev E Stat Nonlin Soft Matter Phys, 2014, 90, (3), pp. 032922
Issue Date:: 2014-09

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Field	Value	Language
dc.contributor.author	Chowdury, A
dc.contributor.author	Kedziora, DJ
dc.contributor.author	Ankiewicz, A
dc.contributor.author	Akhmediev, N
dc.date.accessioned	2023-03-28T21:55:08Z
dc.date.available	2023-03-28T21:55:08Z
dc.date.issued	2014-09
dc.identifier.citation	Phys Rev E Stat Nonlin Soft Matter Phys, 2014, 90, (3), pp. 032922
dc.identifier.issn	1539-3755
dc.identifier.issn	1550-2376
dc.identifier.uri	http://hdl.handle.net/10453/168763
dc.description.abstract	We present the fifth-order equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrödinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.
dc.format	Print-Electronic
dc.language	eng
dc.publisher	AMER PHYSICAL SOC
dc.relation.ispartof	Phys Rev E Stat Nonlin Soft Matter Phys
dc.relation.isbasedon	10.1103/PhysRevE.90.032922
dc.rights	info:eu-repo/semantics/closedAccess
dc.subject	01 Mathematical Sciences, 02 Physical Sciences, 09 Engineering
dc.subject.classification	Fluids & Plasmas
dc.subject.mesh	Motion
dc.subject.mesh	Nonlinear Dynamics
dc.subject.mesh	Quantum Theory
dc.subject.mesh	Nonlinear Dynamics
dc.subject.mesh	Motion
dc.subject.mesh	Quantum Theory
dc.subject.mesh	Motion
dc.subject.mesh	Nonlinear Dynamics
dc.subject.mesh	Quantum Theory
dc.title	Soliton solutions of an integrable nonlinear Schrödinger equation with quintic terms.
dc.type	Journal Article
utslib.citation.volume	90
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	2023-03-28T21:55:07Z
pubs.issue	3
pubs.publication-status	Published
pubs.volume	90
utslib.citation.issue	3

Abstract:

We present the fifth-order equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrödinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.

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http://hdl.handle.net/10453/168763