Periodic, n-soliton and variable separation solutions for an extended (3+1)-dimensional KP-Boussinesq equation.

An extended (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq equation is studied in this paper to construct periodic solution, n-soliton solution and folded localized excitation. Firstly, with the help of the Hirota's bilinear method and ansatz, some periodic solutions have been derived. Secondly, taking Burgers equation as an auxiliary function, we have obtained n-soliton solution and n-shock wave.