Superposition Formula of arbitrary functions to a (3+1)-demensional Boiti–Leon–Manna–Pempinelli equation

Abstract

The (3+1)-dimensional Boiti–Leonon–Manna–Pempinelli equation was studied by using Hirota bilinear method. In this paper, we successfully derived the multi-solutions of this equation consisting of the superpositions of M arbitrary functions. A variety of new solutions can be obtained by choosing different values of the parameter M and test functions f in this paper, i.e., the localized solutions generated by M-positive quadratic functions, the mixed solutions consisting of the localized wave solutions and the kink wave solutions, and the mixed solutions consisting of a trigonometric function and exponential functions. Meanwhile, their corresponding physical plots were displayed to analyze their physical significance and dynamic properties. Some solutions from previous studies were found when M took a specific value and the test functions took particular functions. Thus, the received solutions are more general compared to the previous studies.