Auto-Bäcklund transformation and exact solutions to the generalized Kadomtsev-Petviashvili equation with variable coefficients

By using the extended homogeneous balance method, & new auto-Bäcklund transformation(BT) to the generalized Kadomtsev-Petviashvili equation with variable coefficients (VCGKP) are obtained. And making use of the auto-BT and choosing a special seed solution, we get many families of new exact solutions of the VCGKP equations, which include single soliton-like solutions, multi-soliton-like solutions, and special-soliton-like solutions. Since the KP equation and cylindrical KP equation are all special cases of the VCGKP equation, and the corresponding results of these equations are also given respectively.