The residual symmetry, Bäcklund transformations, CRE integrability and interaction solutions: (2+1)-dimensional Chaffee–Infante equation

Abstract

Abstract In this paper, we consider the (2+1)-dimensional Chaffee–Infante equation, which occurs in the fields of fluid dynamics, high-energy physics, electronic science etc. We build Bäcklund transformations and residual symmetries in nonlocal structure using the Painlevé truncated expansion approach. We use a prolonged system to localize these symmetries and establish the associated one-parameter Lie transformation group. In this transformation group, we deliver new exact solution profiles via the combination of various simple (seed and tangent hyperbolic form) exact solution structures. In this manner, we acquire an infinite amount of exact solution forms methodically. Furthermore, we demonstrate that the model may be integrated in terms of consistent Riccati expansion. Using the Maple symbolic program, we derive the exact solution forms of solitary-wave and soliton-cnoidal interaction. Through 3D and 2D illustrations, we observe the dynamic analysis of the acquired solution forms.