In this present article, we devote our study on (2 + 1)-dimensional Nizhnik-Novikov-Vesselov (NNV) equations. To achieve our goal, we utilize various mathematical methods, namely Lie symmetry method, the Exp-function method and N-soliton solutions methods, and attain exact analytical solutions in numerous forms of the NNV system. Firstly, we generate infinitesimal generators, geometric vector fields, commutation relations of Lie algebra, and one-dimensional optimal system of the NNV equations. By using the Lie symmetry reduction method, the (2 + 1)-dimensional NNV system of equations is reduced to a (1+1)-dimensional partial differential equations (PDEs). Thereafter, we apply the Exp-function method to the reduced NNV equations with the aid of symbolic computation via Mathematica. The exact analytical solutions are obtained in the forms of different wave structures of solitons, doubly solitons, Weierstrass solution, lump-type solitons, bright solitons and dark solitons, paraboli...

中文翻译：

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（2 +1）维NNV方程的Lie对称分析，精确解析解和孤子动力学

在本文中，我们致力于研究（2 +1）维Nizhnik-Novikov-Vesselov（NNV）方程。为了实现我们的目标，我们利用了各种数学方法，即李对称方法，Exp函数函数方法和N孤子解方法，并在多种形式的NNV系统中获得了精确的解析解。首先，我们生成无穷小生成器，几何矢量场，李代数的换向关系以及NNV方程的一维最佳系统。通过使用Lie对称约简方法，将（2 + 1）维NNV方程组简化为（1 + 1）维偏微分方程（PDE）。此后，借助借助Mathematica的符号计算，将Exp函数方法应用于简化的NNV方程。