In this present article, the new [Formula: see text]-dimensional modified Calogero-Bogoyavlenskii-Schiff (mCBS) equation is studied. Using the Lie group of transformation method, all of the vector fields, commutation table, invariant surface condition, Lie symmetry reductions, infinitesimal generators and explicit solutions are constructed. As we all know, an optimal system contains constructively important information about the various types of exact solutions and it also offers clear understandings into the exact solutions and its features. The symmetry reductions of [Formula: see text]-dimensional mCBS equation is derived from an optimal system of one-dimensional subalgebra of the Lie invariance algebra. Then, the mCBS equation can further be reduced into a number of nonlinear ODEs. The generated explicit solutions have different wave structures of solitons and they are analyzed graphically and physically in order to exhibit their dynamical behavior through 3D, 2D-shapes and respective contour plots. All the produced solutions are definitely new and totally different from the earlier study of the Manukure and Zhou (Int. J. Mod. Phys. B 33, (2019)). Some of these solutions are demonstrated by the means of solitary wave profiles like traveling wave, multi-solitons, doubly solitons, parabolic waves and singular soliton. The calculations show that this Lie symmetry method is highly powerful, productive and useful to study analytically other nonlinear evolution equations in acoustics physics, plasma physics, fluid dynamics, mathematical biology, mathematical physics and many other related fields of physical sciences.

中文翻译：

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(2+1)维修正CBS方程孤子解的李对称分析和动力学结构

在本文中，研究了新的 [公式：见正文] 维修正的 Calogero-Bogoyavlenskii-Schiff (mCBS) 方程。使用李群变换方法，构造了所有的向量场、交换表、不变表面条件、李对称约简、无穷小生成元和显式解。众所周知，最优系统包含有关各种类型精确解的建设性重要信息，它还提供对精确解及其特征的清晰理解。[公式：见正文]维 mCBS 方程的对称约简源自李不变代数的一维子代数的最优系统。然后，mCBS 方程可以进一步简化为多个非线性 ODE。生成的显式解具有不同的孤子波结构，并通过图形和物理方式对它们进行分析，以便通过 3D、2D 形状和相应的等高线图展示它们的动态行为。所有产生的解决方案都绝对是新的，并且与 Manukure 和 Zhou 的早期研究完全不同（Int. J. Mod. Phys. B 33, (2019)）。其中一些解决方案是通过行波、多孤子、双孤子、抛物线波和奇异孤子等孤波剖面来证明的。计算表明，这种李对称方法非常强大、高效，可用于分析研究声学物理、等离子体物理、流体动力学、数学生物学、数学物理和物理科学的许多其他相关领域中的其他非线性演化方程。