Bäcklund transformation and interaction solutions of a generalized Kadomtsev–Petviashvili equation with variable coefficients

Abstract

Kadomtsev–Petviashvili (KP) equation is a classical nonlinear evolution equation applied in many fields such as plasma physics, fluid dynamics and engineering. In general, variable coefficients are of value in reflecting the inhomogeneities of media, nonuniformities of boundaries, and external forces. This paper mainly studies some exact solutions of a generalized KP equation with variable coefficients by using Hirota bilinear method. Based on the bilinear form, one-, two-, N-soliton solution, Bäcklund transformation and Lax pair are obtained. With the use of the test function method, lump solution and interaction solutions of lump-stripe and lump-soliton types are constructed, and the structure of the solutions are shown in three-dimensional figures. The analysis on the interaction solutions reveals new dynamic behaviors and periodic evolutions.