Soliton Solutions and Chaotic Dynamics of the Ion-Acoustic Plasma Governed by a (3+1)-Dimensional Generalized Korteweg–de Vries–Zakharov–Kuznetsov Equation

Abstract

This study explores the novel dynamics of the (3+1)-dimensional generalized Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation. A Galilean transformation is employed to derive the associated system of equations. Perturbing this system allows us to investigate the presence and characteristics of chaotic behavior, including return maps, fractal dimension, power spectrum, recurrence plots, and strange attractors, supported by 2D and time-dependent phase portraits. A sensitivity analysis is demonstrated to show how the system behaves when there are small changes in initial values. Finally, the planar dynamical system method is used to derive anti-kink, dark soliton, and kink soliton solutions, advancing our understanding of the range of solutions admitted by the model.

Keywords

• KdV-ZK model
• return map
• fractal dimension
• chaos
• numerical methods