Unveiling solitary and twinning kink solitons in (2+1)-dimensional modified Zakharov-Kuznetsov equation arising in electronics.

In recent years, discovering and examining novel soliton solutions to nonlinear models that emerge in the disciplines of science and engineering have received noticeable fascination from researchers, as these solutions shed light on the models' underlying phenomena. This study goals to establish and evaluate new plethora of soliton solutions in the context of (2+1)-dimensional Modified Zakharov-Kuznetsov Equation (MZKE), which arises in electrical engineering, using a novel analytical tool called the Riccati Modified Extended Simple Equation Method (RMESEM). A mathematical framework for MZKE is first modelled by applying Kirchhoff's law to the nonlinear electrical transmission line circuit. The suggested anstaz RMESEM then generates nonlinear ordinary differential equation (NODE) from the model using a sophisticated wave transformation. To find a new variety of soliton solutions, the resultant NODE is assumed to have a closed form solution that transforms it into a system of nonlinear algebraic equations by substitution. Solving the resultant system using maple yields novel families of soliton solutions for the aimed MZKE in the form of rational, hyperbolic, trigonometric, rational-hyperbolic and exponential functions. Graphical representations of the wave behavior of different soliton solutions are provided by three-dimensional, contour, and two-dimensional graphs. These graphs reveal that the found solitons significantly display the profiles of kink solitons, including bell-shaped, lump-like, twinning, and perturbed kinks. The obtained results contribute to a deeper understanding of the model and its potential applications in related domains by providing useful insights into the dynamics and behavior of the MZKE. Significantly, the results obtained also demonstrate that the proposed transformation-based RMESEM offers a straightforward and trustworthy strategy for exploring soliton phenomena in a wide range of nonlinear equations.