(2+1)维广义浅水波方程的Lax对,Darbuox变换和孤子解

In this paper, the (2+1)-dimensional generalization of shallow water wave equation which can be used to describe the propagation of ocean waves is analytically investigated. With the aid of symbolic computation, we prove that the (2+1)-dimensional generalization of shallow water wave equation has the Painlev'e property under a certain condition and apply the singular manifold method to constructing its Lax pair. Based on the obtained Lax representation, the Darboux transformation is constructed. The first iterated solution, second iterated solution and an N-soliton solution with an arbitrary function are derived with the resulting Darboux transformation. Relevant properties are graphically illustrated, which might be helpful to understanding the propagation processes for ocean waves on shallow waters.