Analytical solutions of (3+1)-dimensional modified KdV–Zakharov–Kuznetsov dynamical model in a homogeneous magnetized electron–positron–ion plasma and its applications

This study examines the dynamical equation of the modified Korteweg–de Vries–Zakharov–Kuznetsov (mKdV-ZK), which is used to describe wave propagation in a dispersive and nonlinear medium. This equation is an extension of the well-known KdV-ZK equation, which has been extensively studied in the literature. In this study, we examine the solitary wave solutions of the (3+1)-dimensional mKdV-ZK equation using two analytical techniques: the generalized [Formula: see text]-expansion approach and the two-variable [Formula: see text]-expansion techniques. As a result, novel soliton solutions in a variety of forms, including Kink- and anti-Kink-type breather waves, dark and bright solitons, Kink soliton and multi-peak solitons, etc. are attained. The solitary wave solutions (which represent the electrostatic field potential), quantum statistical pressures, electric fields and magnetic fields are accomplished with the use of software. These solutions have numerous applications in various areas of physics and other sciences. These results also have applications in electromagnetic wave propagation, nonlinear optics, and plasma physics. Graphical representations of these results have also been presented. These results demonstrate the effectiveness of the two-variable expansion strategy, which will also be useful in solving many other nonlinear models that arise in mathematical physics and several other applied sciences fields. This work contributes to the advancement of novel wave manipulation and control methods, the construction of improved photonic devices for sensing and communications, and plasma confinement in fusion devices, among other uses.