On the solitary wave solutions and physical characterization of gas diffusion in a homogeneous medium via some efficient techniques

This paper aims to determine some novel solitary wave solutions of the Chaffee–Infante equation, which have not yet been presented for this equation. This equation arises in various branches of science and technology, such as plasma physics, coastal engineering, fluid dynamics, signal processing through optical fibers, ion-acoustic waves in plasma, the sound waves, and the electromagnetic waves field. The $$(2+1)$$ -dimensional Chaffee–Infante equation describes the dynamical behavior of gas diffusion in a homogeneous medium. Soliton solutions are obtained for this equation using several computational schemes. Many physical significances are explained by sketching some two-dimensional and three-dimensional diagrams for the acquired solutions in three different types. These figures give us a better understanding of the behavior of these solutions. Moreover, the stability property is investigated based on the Hamiltonian system’s characterizations. The methods provide efficient way for the solving other equations that occur in other branches of science.