Wronskian Form Solutions for a Variable Coefficient Kadomtsev—Petviashvili Equation

Abstract

Starting from a simple transformation, and with the aid of symbolic computation, we establish the relationship between the solution of a generalized variable coefficient Kadomtsev—Petviashvili (vKP) equation and the solution of a system of linear partial differential equations. According to this relation, we obtain Wronskian form solutions of the vKP equation, and further present N-soliton-like solutions for some degenerated forms of the vKP equation. Moreover, we also discuss the influences of arbitrary constants on the soliton and N-soliton solutions of the KPII equation.