Classification of single traveling wave solutions to the nonlinear dispersion Drinfel’d–Sokolov system

Hu, Jinyan

doi:10.1016/j.amc.2012.08.043

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2014

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“…Zhang et al [5] showed some solutions of system (1) under the special parameters via employing the bifurcation method. By means of the complete discrimination system for polynomial method, many solutions of system (1) were acquired in [6].…”

Section: Introductionmentioning

confidence: 99%

Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d-Sokolov System

Cai

Pan

Liu

2014

Abstract and Applied Analysis

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We study the bifurcations of nonlinear waves for the generalized Drinfel’d-Sokolov systemut+(vm)x=0,vt+a(vn)xxx+buxv+cuvx=0calledD(m,n)system. We reveal some interesting bifurcation phenomena as follows. (1) ForD(2,1)system, the fractional solitary waves can be bifurcated from the trigonometric periodic waves and the elliptic periodic waves, and the kink waves can be bifurcated from the solitary waves and the singular waves. (2) ForD(1,2)system, the compactons can be bifurcated from the solitary waves, and the peakons can be bifurcated from the solitary waves and the singular cusp waves. (3) ForD(2,2)system, the solitary waves can be bifurcated from the smooth periodic waves and the singular periodic waves.

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Section: Introductionmentioning

confidence: 99%