Painlevé Analysis and Determinant Solutions of a (3+1)-Dimensional Variable-Coefficient Kadomtsev–Petviashvili Equation in Wronskian and Grammian Form

Abstract

In this paper, the investigation is focused on a (3+1)-dimensional variable-coefficient Kadomtsev–Petviashvili (vcKP) equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the (3+1)-dimensional vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the (3+1)-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant.