Construction Of The Exact Solutions For The(2+1)-dimensional Generalized Shallow Water Wave Equation

Abstract People always pay attention to the exact solutions of nonlinear partial differential equations,it provides a scientific theoretical basis for explaining the nonlinear especial phenomenon in the atmosphere, rivers and seas.In this article, the modified homogeneous balance method, the auxiliary differential expansion and a new simple method are used to solve the (2+1)-Dimensional Generalized shallow water wave equations, and obtains a series of new exact solutions. It includes the kink type solitary wave solutions, tip shaped solitary wave solutions, rational function solutions, trigonometric wave solution, hyperbolic function solutions and other forms of solution. Meanwhile, we solve the symmetric regularized long wave equation and the Bogoyavlenskii’s generalized breaking soliton equation by using the new method. It enriches the exact solutions of the form.