Abstract
In this paper, we introduced and established some group invariant results of [Formula: see text]-dimensional mKdV–Calogero–Bogoyavlenskii–Schiff equation. Using the one-parameter Lie-group of transformations, we explored various closed-form solutions. The procedure minimizes the number of independent variables by one in every proceeding stage leading to form a system of the ordinary differential equations. The nature of solutions is investigated both analytically and physically through their evolutionary profiles by considering adequate choices of arbitrary functions and constants. The obtained results have been plotted with the aid of numerical simulation to obtain a significant appearance of the traced results. Simulation is carried out by taking an adequate option of arbitrary constants and functions, applying MATLAB code through progressing profiles. Wave solutions derived here are positons, multiple solitons, negaton and kink types which are shown through graph analysis.
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