Exact Explicit Solutions of a Nonlinear Evolution Equation
Zhengyong Ouyang *
Department of Mathematics, Foshan University, Guangdong 528000, P.R. China.
Shan Zheng
Guangzhou Maritime College, Guangzhou 510725, P.R. China.
*Author to whom correspondence should be addressed.
Abstract
We employ bifurcation method of dynamical systems to investigate exact traveling wave solutions of a nonlinear evolution equation. We obtain some exact explicit expressions of solitary wave solutions and some new exact periodic wave solutions in parameter forms of Jacobian elliptic function. We point out that the solitary waves are limits of the periodic waves in some sense, the results infer that the periodic waves degenerate solitary waves in some conditions.
Keywords: Bifurcation method, solitary wave solutions, periodic waves solution.