Solitary wave solutions, fusionable wave solutions, periodic wave solutions and interactional solutions of the (3+1)-dimensional generalized shallow water wave equation

Abstract

In this paper, we study exact solutions of the generalized shallow water wave equation. Based on the bilinear equation, we get [Formula: see text]-solitary wave solutions. For special parameters, we find [Formula: see text]-fusionable wave solutions. For complex parameters, periodic wave solutions and elastic interactional solutions of solitary waves with periodic waves are obtained. The properties of obtained exact solutions are also analyzed theoretically and graphically by using asymptotic analysis.