Symmetry analysis, conservation laws and exact soliton solutions for the \((n+1)\)-dimensional modified Zakharov–Kuznetsov equation in plasmas with magnetic fields

This article utilizes the Lie symmetry method to analyze the \((n+1)\) $(n+1)$ -dimensional modified Zakharov–Kuznetsov (mZK) equation, which characterizes weakly nonlinear traveling waves in plasma with a constant magnetic field, comprising cold ions and hot isothermal electrons. The model is also applicable to dusty and magnetized plasma. Lie point symmetries and associated group invariant solutions are computed using Lie group theory, with the underlying equation. The improved \(\tan \bigg (\frac{\Phi (\xi )}{2}\bigg )\) $tan(\frac{\mathrm{\Phi }(\xi )}{2})$ -expansion method is then employed to derive soliton solutions, including hyperbolic, trigonometric, rational, and exponential forms. Graphic interpretations of specific solutions are provided. Nonlinear self-adjointness is used to compute non-local conservation laws in lower dimensions, and conservation laws are developed based on the equation’s formal Lagrangian structure, applying Ibragimov’s theorem. These findings highlight the novelty and reliability of the methodology employed.