Auto-Bäcklund Transformation and Soliton-Type Solutions of the Generalized Variable-Coefficient Kadomtsev--Petviashvili Equation

Using the truncated Painlevé expansion, an auto-Bäcklund transformation and soliton-type solutions of the generalized variable-coefficient Kadomtsev--Petviashvili (GKP) equation are obtained by symbolic computation. Since the cylindrical Korteweg-de Vries (cKdV) equation, the cylindrical KP (cKP) equation and the generalized cKP (GcKP) equation are all special cases of the GKP equation, we can also obtain the corresponding results of these equations.