In soliton theory, the dynamics of solitary wave solutions may play a crucial role in the fields of mathematical physics, plasma physics, biology, fluid dynamics, nonlinear optics, condensed matter physics, and many others. The main concern of this present article is to obtain symmetry reductions and some new explicit exact solutions of the (2 + 1)-dimensional Sharma–Tasso–Olver (STO) equation by using the Lie symmetry analysis method. The infinitesimals for the STO equation were achieved under the invariance criteria of Lie groups. Then, the two stages of symmetry reductions of the governing equation are obtained with the help of an optimal system. Meanwhile, this Lie symmetry method will reduce the STO equation into new partial differential equations (PDEs) which contain a lesser number of independent variables. Based on numerical simulation, the dynamical characteristics of the solitary wave solutions illustrate multiple-front wave profiles, solitary wave solutions, kink wave solitons, oscillating periodic solitons, and annihilation of parabolic wave structures via 3D plots.

中文翻译：

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（2 + 1）维非线性Sharma-Tasso-Olver方程精确解的Lie对称性分析和动力学

在孤子理论中，孤波解的动力学可能在数学物理学，等离子物理学，生物学，流体动力学，非线性光学，凝聚态物理以及许多其他领域中发挥至关重要的作用。本文的主要关注点是使用李对称分析方法获得（2 +1）维Sharma-Tasso-Olver（STO）方程的对称约简和一些新的显式精确解。STO方程的无穷小是在Lie组的不变性准则下实现的。然后，借助最优系统，获得了控制方程对称性简化的两个阶段。同时，这种Lie对称方法会将STO方程简化为新的偏微分方程（PDE），其中包含较少数量的自变量。基于数值模拟，