The new constructive algorithm and symbolic computation applied to exact solutions of nonlinear wave equations

Abstract In this Letter, a new method (called generalized sine-Gordon equation expansion method) is proposed by further studying the famous sine-Gordon equation and using a generalized transformation to seek more types of solutions of nonlinear wave equations. With the aid of symbolic computation, we choose ( 2 + 1 ) -dimensional Burgers equation and the variant Boussinesq equations to illustrate the validity and advantages of the algorithm. As a consequence, more types of new solitary wave solutions, singular solitary wave solutions and doubly periodic solutions are obtained. The algorithm can be also extended to many other nonlinear wave equations.

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