Functional variable method and its applications for finding exact solutions of nonlinear PDEs in mathematical physics

摘要

The functional variable method is a powerful mathematical tool for obtaining exact solutions of nonlinear evolution equations in mathematical physics. In this paper, the functional variable method is used to establish exact solutions of the (2+1)-dimensional Kadomtsov-Petviashivilli-Benjamin-Bona-Mahony (KP-BBM) equation, the (2+1)-dimensional Konopelchenko-Dubrovsky equation, the (3+1)-dimensional Burgers equation and the (3+1)- dimensional Jimbo-Miwa equation. The exact solutions of these four nonlinear equations including solitary wave solutions and periodic wave solutions are obtained. It is shown that the proposed method is effective and can be applied to many other nonlinear evolution equations. Comparison between our results obtained in this paper and the well-known results obtained by different authors using different methods are presented.