Breather waves and rational solutions in the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Abstract

We consider the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation, which can be used to describe the incompressible fluid. We derive the Hirota bilinear form of the equation via the Bell polynomial. By using Hirota’s direct method, we obtain the N-soliton wave solutions of the equation. Based on the resulting Hirota’s bilinear equation, we directly derive the breather wave solutions and rational solutions of the equation. Moreover, we employ the long wave limit method to derive the first-order and second-order rational solutions. In order to better understand the dynamical behaviors of the equation, we provide some graphical analyses to discuss the properties for the dynamic behaviors of these solutions.