Lump solution and lump-type solution to a class of water wave equation

Abstract

In the field of nonlinear sciences, the theory of solitons has long been regarded as one of the most significant and effective areas of research. In this research field, there are many efficient techniques for solving partial differential equations. The main concern of the present work is to obtain lump and lump-type solutions to the generalized water wave equation utilizing Hirota’s bilinear method. These solutions include some different interaction forms of quadratic, a lump solution with hyperbolic cosine and exponential, and a quadratic term with Jacobi elliptic functions. Further, we graphically present the nature of the collision solutions of the equation in 3D and contour plots. To the best of our knowledge, the employed technique in this contribution has not been applied to the main equation of the paper, in the existing literature. The findings provide an efficient method to investigate analytical solutions to other nonlinear equations.