Volume no :1, Issue no: 1, February (2009)

Journal of Pure and Applied Mathematics: Advances and Applications

BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS FOR A CLASS OF GENERALIZED NONLINEAR EVOLUTION EQUATIONS

Author's: Jie Zheng, Shengqiang Tang and Wentao Huang
Pages: [47] - [58]
Received Date: November 24, 2008
Submitted by:

Abstract

By using the bifurcation theory of dynamical systems to a class of generalized nonlinear evolution equations, the existence of solitary wave solutions, kink and anti-kink wave solutions, periodic cusp wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions is obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of the above travelling wave solutions are determined.

Keywords

solitary wave solution, periodic wave solution, smooth wave, generalized nonlinear evolution equation.