Dynamics of invariant solutions of mKdV-ZK arising in a homogeneous magnetised plasma

Classical Lie symmetry analysis is proposed to get a new variety of similarity solutions to a nonlinear (3+1)-modified Korteweg de Vries-Zakharov–Kuznetsov equation. The equation is often used to control the type of weakly nonlinear ion-acoustic waves in a homogeneous magnetised electron-positron plasma. In a magnetised plasma, including some hot and cold ions, such waves exist. By comparing the results reported earlier, new variety of analytical solutions are created and validated. Trigonometric, hyperbolic, rational, and exponential solutions of various types are derived. To prove their physical significance, animation profiles are plotted using MATLAB. Dominated dynamical behaviour of the animation profile is represented in each case. Electrostatic potential dynamics reveal elastic single solitons to multi solitons, elastic multi solitons, kink to stationary, and bell-shaped to asymptotic behaviour. Equations (13) and (21) in this study that were solved trivially can lead to more research in this area.