Smooth Exact Traveling Wave Solutions Determined by Singular Nonlinear Traveling Wave Systems : Two Models

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Detail(s)

Original languageEnglish
Article number1950047
Journal / PublicationInternational Journal of Bifurcation and Chaos
Volume29
Issue number4
Publication statusPublished - Apr 2019

Abstract

For a singular nonlinear traveling wave system of the first class, if there exist two node points of the associated regular system in the singular straight line, then the dynamics of the solutions of the singular system will be very complex. In this paper, two representative nonlinear traveling wave system models (namely, the traveling wave system of Green-Naghdi equations and the traveling wave system of the Raman soliton model for optical metamaterials) are investigated. It is shown that, if there exist two node points of the associated regular system in the singular straight line, then the singular system has no peakon, periodic peakon and compacton solutions, but rather, it has smooth periodic wave, solitary wave and kink wave solutions.

Research Area(s)

  • Integrable system, exact solution, homoclinic orbit, heteroclinic orbit, periodic solution, Green-Naghdi equation, Raman soliton model, SOLITONS, EQUATIONS, WATER