Traveling wave structures of the (2+1)-dimensional b-type kadomtsev-petviashvili equation

Abstract The fast development of technology and science increases the demand on solving quite complicated nonlinear partial differential equations (NLPDEs) in order to simulate their physical phenomena. In this paper, the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation with its abundant traveling wave solutions is investigated in detail , which derived from the calculus of pseudodifferential operators. The bilinear form for this equation is shown after taking the traveling wave transformation and the formal traveling wave solution is constructed through two auxiliary functions. Therefore, the typical traveling wave and periodic wave structures are naturally presented, the special few-cycle-pulse solitons and some soliton molecules are also found. Some significant solutions have been graphically elaborated in a form of 2D, 3D and contour plots by selecting the appropriate parameters in order to provide a better physical illustration and understanding of the dynamical physical properties of this model.