On the study of interaction phenomena to the (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

Abstract

The (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation which consists of the KdV equation and the SK equation is the subject of investigation in this study. The studied equation has rich physical meaning in nonlinear waves. The KdV- type equations hold great importance as a prototypical representation of an infinite-dimensional system that is completely integrable and exactly solvable in the context of nonlinearity. The KdV equation is utilized to describe shallow water waves in a density-stratified ocean, which exhibit weak and nonlinear interactions with long internal waves. The Hirota bilinear method has been used with the support of various test functions. For the purpose of analyzing the governing equation, numerous solutions are secured, including breathers and two-wave solutions. Breather waves refer to solitary waves that exhibit both partial localization and periodic structure in either space or time. Breathers serve crucial functions in nonlinear physics and have been observed in various physical domains, including optics, hydrodynamics, and quantized superfluidity. To visually represent the results, a range of graphs with unique shapes are generated in accordance with the specified parameter values. The computational intricacies and outcomes underscore the technique’s efficacy, simplicity and transparency, demonstrating its suitability for numerous types of static and dynamic nonlinear equations pertaining to evolutionary phenomena in computational physics, in addition to other research and practical domains. The physical properties of solutions and the collision-related components of various nonlinear physical processes are illustrated with these results.