Chaotic dynamics and exact solutions for (3+1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff model

Abstract

We apply the Hirota bilinear method to systematically derive breather-kink wave, double-solitary wave and rogue wave solutions for the (3+1)-dimensional KdV–Calogero–Bogoyavlenskii–Schiff equation, which describes nonlinear phenomena in fluid dynamics and plasma physics. The validity and behavior of these solutions are demonstrated through graphical analysis. Moreover, we comprehensively analyze the chaotic dynamics in a 3D perturbed system through chaos detecting tools. These findings hold significant importance for the discipline, providing crucial insights into the complex dynamics of the KdV-CBS equation. We hope that our research results will assist researchers in comprehending the nonlinear phenomena associated with shallow water waves in oceans, rivers, and coastal areas.