Novel exploration of nonlinear waves of a generalized (2+1)-dimensional extended Boussinesq equation: solitons, breathers and periodic background waves

Abstract

In this analytical investigation, we explore various solutions for a generalized and extended Boussinesq (eBO) equation in (2+1)-dimensions. It applies a problem-solving approach known as the generalized exponential rational function technique, which first transforms the equation into a simplified ordinary differential equation under a wave transformation. It considers the trial function as a rational function involving exponential functions for the simplified equation. With these considerations, the desired analytic solutions, which include solitons, breathers, kink-solitons, and periodic background waves, are explored for the investigated equation. Under arbitrary choices for the constants in the rational function, it analyzes different families with several computed cases to obtain the solutions for a rational function, which provides the general solution of the studied eBO equation using back substitution. We graphically explore the obtained solutions in the form of different solitons, breathers, and periodic waves, with arbitrary choices for the involved constant coefficients. It discusses the work's significant importance and the dynamic behavior of the obtained solution. The investigated eBO equation is important in nonlinear sciences and has many physical applications. It provides insights into the multi-dimensional waves and solitons interactions in applied mathematics and physics and many other fields such as optics, fluid dynamics, geophysics, and plasma physics.