This paper studies the potential form of the 3D potential Yu–Toda–Sasa–Fukuyama equation through the perspective of Lie symmetry analysis. This technique combined with symbolic computations does prove that the general Lie operator depends on five parameters and six independent arbitrary functions that are variable in respect to time. The group invariant solutions associated to some 1D subalgebras are systematically construct and they do involve arbitrary functions. When these functions are expressed under several specific forms, the associated wave solutions possess multiple structures. Graphical representations of some particular solutions are as well provided. As far as we know such general solutions are presented here for the first time and do indicate the symmetry method to be applied in order to solve other multidimensional, integrable, or nonintegrable nonlinear dynamical models.

中文翻译：

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基于对称技术的 3D 势 Yu–Toda–Sasa–Fukuyama 方程的多重不变量解

本文从李对称分析的角度研究了 3D 势的 Yu-Toda-Sasa-Fukuyama 方程的势形式。这种与符号计算相结合的技术确实证明了一般的李算子取决于五个参数和六个独立的随时间变化的任意函数。与一些一维子代数相关的群不变解是系统构造的，它们确实涉及任意函数。当这些函数以几种特定的形式表示时，相关的波解就具有多种结构。还提供了一些特定解决方案的图形表示。据我们所知，这样的一般解决方案是第一次在这里提出，并且确实表明了为了解决其他多维、可积、