Abstract
An exteded mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinear partial differential equations(PDEs).The key idea of this method is to take full advantage of the simple algebraic mapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein-Gordon equation.This is applied to solve a system of variant Boussinesq equations,As a result,many explicit and exact solutions are obtained,including solitary wave solutions,periodic wave solutions,Jacobian elliptic function solution solutions and other exact solutions.
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