Qualitative behavior and traveling wave solutions of the (n + 1)-dimensional Camassa–Holm Kadomtsev–Petviashvili equation

This study investigates the dynamics of the [Formula: see text]-dimensional Camassa–Holm Kadomtsev–Petv iashvili equation by applying the galilean transformation to the model, leading to the consideration of a planar dynamical system. The research includes a detailed analysis of bifurcation and sensitivity within the system. Furthermore, when an external force is applied, the system exhibits chaotic behavior. Chaotic patterns are identified using various chaos detection tools. A range of techniques, including time series analysis, return map, fractal dimension, Lyapunov exponents, bifurcation diagrams, multistability, poincare map, and sensitivity analysis, are employed to explore the system’s behavior under specified initial conditions. The Hamiltonian function is calculated and plotted for the unperturbed system. The study also explores multi-stability, revealing the coexistence of multiple stable orbits. Additionally, the extended hyperbolic function method is utilized to compute various solitonic structures across different parameter sets, resulting in both real and complex solutions. The effect of wave velocity on these solutions is also observed. These findings offer a novel contribution to the understanding of the dynamics of the equation, significantly advancing our knowledge of nonlinear wave models.