Wronskian and Grammian Determinant Solutions for a Variable-Coefficient Kadomtsev–Petviashvili Equation

Abstract

In this paper, we derive the bilinear form for a variable-coefficient Kadomtsev–Petviashvili-typed equation. Based on the bilinear form, we obtain the Wronskian determinant solution, which is proved to be indeed an exact solution of this equation through the Wronskian technique. In addition, we testify that this equation can be reduced to a Jacobi identity by considering its solution as a Grammian determinant by means of Pfaffian derivative formulae.