A novel investigation of extended (3+1)-dimensional shallow water wave equation with constant coefficients utilizing bilinear form

Abstract

The aim of this research is to investigate new soliton solutions for the shallow water wave equation in an extended (3+1) dimensional space with constant coefficients. The application of this equation is relevant to the analysis of water body dynamics in seas and oceans. Bäcklund transform for the system is constructed from the bilinear form and rational as well exponential traveling wave solutions are analyzed to obtain kink and singular kink solitons. The Hirota bilinear form is further utilized to construct complexiton solutions through extended transformed rational function method. Appropriate parameter values are selected to create 3D and 2D graphical representations, as well as corresponding density plots, for the physical characterization of certain reported results. The obtained results of this research demonstrate how to use discussed approaches for addressing various real world problems described by nonlinear models.