Wave Dynamics and Electromagnetic Influences on Propagation in the (3+1)-Dimensional Modified KdV-Zakharov–Kuznetsov Equation: Theoretical Insights and Applications

This study focuses on understanding wave propagation in dispersive and nonlinear media by analyzing the dynamical behavior of the modified KdV-Zakharov-Kuznetsov (mKdV-ZK) equation. Building on the extensively researched KdV-ZK equation, this paper examines solitary wave solutions of the (3+1)-dimensional mKdV-ZK equation using the newly extended modified Sardar sub-equation method. As a result, a diverse array of novel soliton solutions is obtained, including multi-peak solitons, kink and anti-kink waves, dark and bright solitons, and breather waves. These solitary wave solutions are derived for various physical quantities such as electrostatic field potential, quantum statistical pressures, electric fields, and magnetic fields. The solutions are presented graphically, demonstrating their applicability across numerous domains in physics and other scientific fields. The efficiency of the suggested approach is highlighted, offering potential for solving a wide range of nonlinear wave systems in applied science and mathematical physics.