Painlevé Property and New Analytic Solutions for a Variable-Coefficient Kadomtsev–Petviashvili Equation with Symbolic Computation

Abstract

A variable-coefficient Kadomtsev–Petviashvili equation is investigated. The Painlevé analysis leads to its explicit Painlevé-integrable conditions. An auto-Bäcklund transformation and the bilinear form are presented via the truncated Painlevé expansion and symbolic computation. Several families of new analytic solutions are presented, including the soliton-like and periodic solutions.