BIFURCATION, EXACT SOLUTIONS AND NONSMOOTH BEHAVIOR OF SOLITARY WAVES IN THE GENERALIZED NONLINEAR SCHRÖDINGER EQUATION-Reference-Cited by-同舟云学术

BIFURCATION, EXACT SOLUTIONS AND NONSMOOTH BEHAVIOR OF SOLITARY WAVES IN THE GENERALIZED NONLINEAR SCHRÖDINGER EQUATION

Published:2005-10 Issue:10 Volume:15 Page:3295-3305
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

WANG WEI¹,SUN JIANHUA¹,CHEN GUANRONG²

Affiliation:

1. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

2. Department of Electronic Engineering, City University of Hong Kong, P. R. China

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)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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127405013897

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