A class of exact solutions of the BBM equations

Abstract

Solutions of nonlinear partial differential equations are hard to be solved generally. In this paper, BBM equation is transformed into the system of algebraic equations, and their coefficients can be easily determined by the homogeneous balance method by means of one-dimensional cubic nonlinear Klein-Gordon equation. Then, the exact solutions of BBM equation is successfully obtained. The solutions contain triangular periodic solutions, Jacobi elliptic function solutions, and so on. The method in the paper can be used to solve other nonlinear evolution equations. © 2011 Springer-Verlag Berlin Heidelberg.