Unraveling Symmetry, Bifurcation Dynamics, and Exotic Attractors Analysis to the (3+1)‐D Modified KdV‐Zakharov‐Kuznetsov Model

ABSTRACT This paper is concerned with a modified ‐dimensional Korteweg‐de Vries (KdV)‐Zakharov‐Kuznetsov (ZK) model, which is a sophisticated model for inherently nonlinear physical systems. First, using the Lie symmetry approach, we determine the Lie symmetries of the model and present the commutator and adjoint table of the symmetries, which gives a comprehensive understanding of the symmetry structure of the equation. Additionally, we investigate a number of dynamical systems theory concepts, including bifurcation, equilibrium points, chaotic behavior, Poincaré maps, Lyapunov exponents, time series analysis, return maps, and heterogeneous recurrence maps. Moreover, we also conduct sensitivity and multivariable analysis, with an emphasis on how parameters affect the dynamics of the system. In order to investigate wave behavior, we construct solitary waves from various families by employing the Sardar sub‐equation (SSE) method to get analytical solutions. These solutions include periodic, combo, chirped, bright, mixed dark‐bright, dark, and kink soliton types. We use the computational software MATLAB to graphically present the spatial architecture and key physical properties of these exact solutions. A fuller comprehension of the wave dynamics in such systems is made possible by the results, which offer insightful information about the underlying nonlinear phenomena.