New exact periodic solitary-wave solutions for the (3+1)(3+1)-dimensional generalized KP and BKP equations

The extended homoclinic test approach (EHTA) is a straightforward and efficient method to solve nonlinear partial differential equations. In this paper, new exact solutions including kinky periodic solitary-wave solutions, periodic soliton solutions and periodic kink solutions for the (3+1)(3+1)-dimensional generalized Kadomtsev–Petviashvili (KP) and B-type Kadomtsev–Petviashvili (BKP) equations are obtained. Moreover, the strangely mechanical features of these wave solutions are investigated. These solutions enrich the variety of the dynamics of higher-dimensional nonlinear wave field.