A series of travelling wave solutions for two variant Boussinesq equations in shallow water waves

Abstract

A new algebraic method is devised to uniformly construct a series of new travelling wave solutions for two variant Boussinesq equations. The solutions obtained in this paper include soliton solutions, rational solutions, triangular periodic solutions, Jacobi and Weierstrass doubly periodic wave solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with most existing tanh methods, the proposed method gives new and more general solutions. More importantly, the method provides a guideline to classify the various types of the solution according to some parameters.