What question did this study set out to answer?

The research aims to develop a unified framework for analyzing the modified Zakharov–Kuznetsov equation and its wave solutions.

Chaotic transitions and multistable regimes in a nonlinear wave model through hybrid analytical–numerical techniques

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This work demonstrates chaotic behavior and multistable solutions in a nonlinear wave model, suggesting new insights for complex systems.

The research aims to develop a unified framework for analyzing the modified Zakharov–Kuznetsov equation and its wave solutions.
Combined exact solution construction with dynamical systems analysis
Utilized the modified Khater method and Sardar subequation technique
Derived various families of traveling wave solutions through MATLAB simulations
Reformulated the mZK equation as a planar dynamical system
Classified qualitative features using phase portraits
Identified new families of solitary wave solutions including trigonometric and hyperbolic forms
Demonstrated bifurcation and chaotic behavior in the system with periodic external forcing
Classified system features with centers, saddles, and cusps in phase portraits
Highlighted the system's sensitivity to parameter variations and multistability

Iqbal et al. (2026) studied this question.

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