On the exact soliton solutions and different wave structures to the (2+1) dimensional Chaffee–Infante equation

Abstract

Nonlinear phenomena observed in diverse scientific disciplines, including fluid dynamics, plasma physics, and biology, are frequently described by partial differential equations (PDEs). Among these PDEs, the Chaffee–Infante equation holds considerable importance and finds applications in various scientific and engineering domains. The focus of this research article revolves around the exploration of closed-form solitary wave solutions for this significant nonlinear evolution equation (NLEE) through the utilization of two efficient techniques. By employing rigorous analysis and computation, our study presents a wealth of soliton solutions and thoroughly investigates their physical implications by examining parameter values and constructing illustrative figures. In-depth exploration of trigonometric, hyperbolic, and rational expression solution forms enables a comprehensive understanding of the intricate dynamics exhibited by plasma behavior. Through the consideration of diverse solution possibilities, this research contributes to an enhanced comprehension of the inherent complexities within plasma systems. In this paper, we have put all the obtained solutions in the main equation and found that all the solutions are correct. This provides strong evidence for the validity of our proposed method and its ability to accurately solve the considered problem. The methods employed in this study distinguish themselves by their simplicity, reliability, and ability to generate novel solutions for nonlinear partial differential equations within the realm of mathematical physics.