In the present article, Lie group of point transformations method is successfully applied to study the invariance properties of the $$(2+1)$$ -dimensional Pavlov equation. Applying the Lie symmetry method, we strictly obtain the infinitesimals, vector fields, commutation relation and several interesting symmetry reductions of the equation. The explicit exact solutions are derived under some limiting conditions imposed on the infinitesimals $$ \xi $$ , $$\phi $$ , $$ \tau $$ and $$ \eta $$ . Then, the Pavlov equation is transformed into a number of nonlinear ODEs through several symmetry reductions. These new exact solutions are more general and entirely different from the work of Kumar et al (Pramana – J. Phys.94: 28 (2020)). The obtained invariant solutions are examined analytically as well as physically through numerical simulation by giving free alternative values of arbitrary functions and constants. Consequently, graphical representations of all these solutions are studied and demonstrated in 3D-graphics and the corresponding contour plots. Interestingly, the solution profiles show the annihilation of three-dimensional parabolic profile, doubly soliton and elastic multisolitons and nonlinear wave nature form.

中文翻译：

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(2 $$+$$ 1)维巴甫洛夫方程孤子解的李对称约简和动力学

本文成功地应用李群点变换方法研究了$$(2+1)$$维巴甫洛夫方程的不变性。应用李对称方法，我们严格地获得了方程的无穷小、向量场、对易关系和几个有趣的对称约简。显式精确解是在对无穷小 $$ \xi $$ 、 $$\phi $$ 、 $$ \tau $$ 和 $$ \eta $$ 施加的一些限制条件下导出的。然后，通过几次对称约简，将巴甫洛夫方程转化为多个非线性常微分方程。这些新的精确解更通用，并且与 Kumar 等人的工作完全不同（Pramana – J. Phys.94: 28 (2020)）。通过给出任意函数和常数的自由替代值，通过数值模拟分析和物理检查获得的不变解。因此，所有这些解决方案的图形表示都在 3D 图形和相应的等高线图中进行了研究和演示。有趣的是，解剖面显示了三维抛物线剖面、双孤子和弹性多孤子以及非线性波性质形式的湮灭。