Dynamical Nonlinear Modified Korteweg–de Vries Equation Arising in Plasma Physics and Its Analytical Wave Solutions

The focus of our work was to discuss the analytical treatment of (mK-dV) model as a result of which we have found some new and more general families of exact solutions which have potential applications to read the qualitative analysis of many nonlinear wave phenomena in a more exact manner, further these results have a high impact to develop the theories of soliton dynamics, adiabatic parameter dynamics and in quantum mechanics. We have also discussed the analytical analysis of two dimensional modified Korteweg-de Vries (mK-dV) equation arising in plasma physics that governs the ion-acoustic solitary waves for their asymptotic behavior because of the trapping of electrons using auxiliary equation mapping method. We have obtained some quite general and new variety of exact travelling wave solutions using this technique, which are collecting some kind of semi half bright, bright, dark, semi half dark, doubly periodic, combined, periodic, half hark and half bright via three parametric values, which is our technique's primary point of difference. These results are highly applicable to develop new theories of quantum mechanics, biomedical problems, soliton dynamics, plasma physics, nuclear physics, optical physics, fluid dynamics, electromagnetism, industrial studies, mathematical physics, biomedical problems, and in many other natural and physical sciences. For detailed physical dynamical representation of our results we have shown them with graphs in different dimensions via Mathematica to get more understanding of different new dynamical shapes of solutions.