Auto-Bäcklund transformation and exact solutions of the generalized variable-coefficient Kadomtsev–Petviashvili equation

Based on the idea of the homogeneous balance (HB) method, an auto-Bäcklund transformation (BT) to the generalized variable-coefficient Kadomtsev–Petviashvili (GvcKP) equation is obtained with symbolic computation. By the use of the auto-BT and the ε-expansion method, we can obtain a soliton-like solution including N-solitary wave of the GvcKP equation. Especially, we get a soliton-like solution including two-solitary wave as an illustrative example in detail. Since the cylindrical KP (cKP) equation, the generalized cKP (GcKP) equation and the spherical KP (SKP) equation are all special cases of the GvcKP equation, we can also obtain the corresponding results of these equations respectively.