Abundant analytical soliton solutions and Evolutionary behaviors of various wave profiles to the Chaffee–Infante equation with gas diffusion in a homogeneous medium

Abstract

The generalized exponential rational function method is used in this work to obtain a variety of rich families of analytical soliton solutions and to exemplify the dynamics of solitonic structures of the (2+1)-dimensional ChaffeeInfante (CI) equation. This CI equation is a well-known reaction–diffusion equation that can describe the physical process of mass transport and particle diffusion and has been widely used in fluid dynamics, electromagnetic wave fields, high-energy physics, fluid mechanics, coastal engineering, and ion-acoustic waves in plasma physics, optical fibers, and other disciplines. The GERF method is successfully used to derive closed-form analytic solutions to the CI equation, including rational, exponential, trigonometric, and hyperbolic function solutions. The CI equation has indeed been observed to have bright and dark solitons, singular and combined singular soliton profiles, periodic oscillating nonlinear waves, and kink-wave profiles. Furthermore, three-dimensional graphical representations are presented to depict the dynamical behavior of the achieved solutions. We can better understand the dynamical properties and structures of these solutions by using these three-dimensional postures. This technique could be used to solve a wide variety of higher-dimensional nonlinear equations confronted in mathematical physics and applied sciences.