摘要
This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method.
This paper is concerned with the （2＋1）-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the （2＋1）-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method.
基金
Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 11505090
Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No.BS2015SF009
the doctorial foundation of Liaocheng University under Grant No.31805
