Conserved Vectors and Analytical Solutions of the (2+1)-Dimensional Modified Zakharov-Kuznetsov Model Arising in Electrical Engineering

Abstract This paper examines the (2+1)-dimensional modified Zakharov-Kuznetsov equation, a nonlinear model arising in electrical engineering used to describe weakly nonlinear ion-acoustic waves in a plasma subjected to a uniform magnetic field. The model finds relevance in various domains such as nonlinear optics, plasma physics and fluid dynamics investigations. Thus, the main objective is to obtain novel analytical solutions by studying the model from a Lie group analysis standpoint, a methodological approach that has not been previously reported for this equation. An optimal system of one-dimensional subalgebras is constructed, from which similarity reductions and corresponding group-invariant solutions are derived. Several ansatz-based techniques are then employed to generate analytical solutions of the reduced equations. The analytical solutions are visualized through three-dimensional, two-dimensional, and density plots, demonstrating a variety of wave behaviours under appropriate choices of arbitrary constants and admissible parameter ranges. In addition, conserved vectors associated with the governing equation are derived using the multiplier method. These results will provide deeper insight into the structure and dynamics of the model and support further analytical and numerical studies. The validity of all the results presented in this study have been examined successfully through the use of the symbolic computation software Wolfram Mathematica.