Dynamical analysis and soliton solutions of the Vakhnenko–Parkes equation with power-law nonlinearity

Abstract

In this paper, we focus on the dynamical analysis and soliton solutions of the Vakhnenko–Parkes (VP) equation. Initially, an appropriate transformation is applied to the VP equation to reduce it to a nonlinear ordinary differential equation. Subsequently, a Galilean transformation is employed to obtain the corresponding dynamical system. The Hamiltonian structure and sensitivity analysis are investigated to better understand the considered model. Furthermore, the Hamiltonian structure of the system is derived, and the sensitivity of the model with respect to key parameters is examined. An external forcing term is then introduced to explore the chaotic dynamics of the system, with particular emphasis on the effects of amplitude and frequency variations. Finally, soliton solutions of the model are derived using the direct algebraic method, and the obtained results are visualized via two-dimensional, three-dimensional, and contour plots to analyze the influence of wave speed.