Soliton solutions and lump-type solutions to the (2+1)-dimensional Kadomtsev-Petviashvili equation with variable coefficient

Abstract

In this article, the integrability, bilinear form, N-soliton solutions, lump solutions and rational function solutions of (2+1)-dimensional Kadomtsev-Petviashvili equation with variable coefficient (vcKP) are investigated. This has important implications for mathematicians and physicists to solve problems related to long water waves. The equation is proved to be Painlevé integrable by Painlevé analysis. With the help of Hirota bilinear method, the bilinear form of vcKP is obtained. Based on the bilinear form, the forms of four different types of solutions are constructed. In addition, taking the long wave limit method on two-soliton solutions, three-soliton solutions and four-soliton solutions to construct the lump solutions and the rational function solutions. As a result, some new solutions of vcKP are obtained, such as soliton solutions, lump solutions and interaction of different kinds of solutions. To describe better the change in solution with time, the dynamical behaviours of the exact solutions to the (2+1)-dimensional vcKP are analysed. The influence of parameters on the soliton solutions is analyzed. Moreover the evolution of several types of solutions is investigated depending on the change in time.