Bifurcation, exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schrödinger equation

Wei Wang; Jianhua Sun; Guanrong Chen

doi:10.1142/S0218127405013897

Bifurcation, exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schrödinger equation

Wei Wang, Jianhua Sun, Guanrong Chen

Department of Electrical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

4 Citations (Scopus)

Abstract

In this paper, the generalized nonlinear Schrödinger equation (GNLS) is studied. The bifurcation of solitary waves of the equation is discussed first, by using the bifurcation theory of planar dynamical systems. Then, the respective numbers of solitary waves are derived under different conditions on the equation parameters. Exact solutions of smooth solitary waves are obtained in the explicit form of a(ξ)e^{i(ψ(ξ)-ωt)} ξ = x -vt by qualitatively seeking the homoclinic and heteroclinic orbits for a class of Liénard equations. Finally, nonsmooth solitary wave solutions of the GNLS are investigated. © World Scientific Publishing Company.

Original language	English
Pages (from-to)	3295-3305
Journal	International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume	15
Issue number	10
DOIs	https://doi.org/10.1142/S0218127405013897
Publication status	Published - Oct 2005

Research Keywords

Bifurcation
Exact solution
Nonsmooth behavior
Schrödinger equation
Solitary wave

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10.1142/S0218127405013897

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@article{d47728914eb34740837f6c6e4f944275,

title = "Bifurcation, exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schr{\"o}dinger equation",

abstract = "In this paper, the generalized nonlinear Schr{\"o}dinger equation (GNLS) is studied. The bifurcation of solitary waves of the equation is discussed first, by using the bifurcation theory of planar dynamical systems. Then, the respective numbers of solitary waves are derived under different conditions on the equation parameters. Exact solutions of smooth solitary waves are obtained in the explicit form of a(ξ)ei(ψ(ξ)-ωt) ξ = x -vt by qualitatively seeking the homoclinic and heteroclinic orbits for a class of Li{\'e}nard equations. Finally, nonsmooth solitary wave solutions of the GNLS are investigated. {\textcopyright} World Scientific Publishing Company.",

keywords = "Bifurcation, Exact solution, Nonsmooth behavior, Schr{\"o}dinger equation, Solitary wave",

author = "Wei Wang and Jianhua Sun and Guanrong Chen",

year = "2005",

month = oct,

doi = "10.1142/S0218127405013897",

language = "English",

volume = "15",

pages = "3295--3305",

journal = "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering",

issn = "0218-1274",

publisher = "World Scientific",

number = "10",

}

Bifurcation, exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schrödinger equation. / Wang, Wei; Sun, Jianhua; Chen, Guanrong.
In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 15, No. 10, 10.2005, p. 3295-3305.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

TY - JOUR

T1 - Bifurcation, exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schrödinger equation

AU - Wang, Wei

AU - Sun, Jianhua

AU - Chen, Guanrong

PY - 2005/10

Y1 - 2005/10

N2 - In this paper, the generalized nonlinear Schrödinger equation (GNLS) is studied. The bifurcation of solitary waves of the equation is discussed first, by using the bifurcation theory of planar dynamical systems. Then, the respective numbers of solitary waves are derived under different conditions on the equation parameters. Exact solutions of smooth solitary waves are obtained in the explicit form of a(ξ)ei(ψ(ξ)-ωt) ξ = x -vt by qualitatively seeking the homoclinic and heteroclinic orbits for a class of Liénard equations. Finally, nonsmooth solitary wave solutions of the GNLS are investigated. © World Scientific Publishing Company.

AB - In this paper, the generalized nonlinear Schrödinger equation (GNLS) is studied. The bifurcation of solitary waves of the equation is discussed first, by using the bifurcation theory of planar dynamical systems. Then, the respective numbers of solitary waves are derived under different conditions on the equation parameters. Exact solutions of smooth solitary waves are obtained in the explicit form of a(ξ)ei(ψ(ξ)-ωt) ξ = x -vt by qualitatively seeking the homoclinic and heteroclinic orbits for a class of Liénard equations. Finally, nonsmooth solitary wave solutions of the GNLS are investigated. © World Scientific Publishing Company.

KW - Bifurcation

KW - Exact solution

KW - Nonsmooth behavior

KW - Schrödinger equation

KW - Solitary wave

UR - http://www.scopus.com/inward/record.url?scp=29244487901&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-29244487901&origin=recordpage

U2 - 10.1142/S0218127405013897

DO - 10.1142/S0218127405013897

M3 - RGC 21 - Publication in refereed journal

SN - 0218-1274

VL - 15

SP - 3295

EP - 3305

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

IS - 10

ER -

Bifurcation, exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schrödinger equation

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