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

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