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 Hirita bilinear method. In this paper, we successfully derived the multi-solutions of this equation by superposition $M$-arbitrary functions. Some solutions from previous studies were found when $M$ took a specific value and the test functions took particular functions. Thus, the recieved solutions were more general compared to the previous studies. 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 are displayed to analyze their physical significance and dynamic properties.