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.

中文翻译：

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基于李对称分析的 mKdV–Calogero–Bogoyavlenskii–Schiff 方程的孤波解

在本文中，我们介绍并建立了[公式：见正文]维mKdV-Calogero-Bogoyavlenskii-Schiff方程的一些群不变结果。使用单参数李群变换，我们探索了各种封闭形式的解决方案。该程序在每个程序阶段将自变量的数量减少一个，从而形成一个常微分方程组。通过考虑采用足够的任意功能和常量，通过它们的进化配置来研究解决方案的性质。所获得的结果已在数值模拟的帮助下绘制出来，以获得跟踪结果的显着外观。Simulation is carried out by taking an adequate option of arbitrary constants and functions, 通过进度配置文件应用 MATLAB 代码。这里导出的波解是通过图形分析显示的位置、多孤子、负子和扭结类型。