Hybrid and physical interaction phenomena solutions to the Hirota bilinear equation in shallow water waves theory

Abstract

The purpose of this research paper is to investigate the (3+1)-dimensional Hirota bilinear equation that arises in nonlinear waves in fluid dynamics, plasma physics and shallow water waves. We use Hirota's bilinear approach and a long-wave method to explore the dynamical features of the suggested equation. Multiple M-lump waves mixed with soliton solutions are constructed. Also, the breather wave and its interaction with one-soliton and M-lump waves are derived. These solutions are believed to play a role in understanding the dynamical aspects of the (3+1)-dimensional Hirota bilinear equation.