Abstract

A system of equations of two-dimensional shallow water over an uneven bottom is considered. An overdetermined system of equations for finding the corresponding symmetries is obtained. The compatibility of this overdetermined system of equations is investigated. A general form of the solution of the overdetermined system is found. The kernel of the symmetry operators is found. The cases of kernel extensions of symmetry operators are presented. The results of group classification indicate that the system of equations of two-dimensional shallow water over an uneven bottom cannot be linearized by point transformation, in contrast to the system of equations of one-dimensional shallow water in the cases of horizontal and inclined bottom profiles.

中文翻译：

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底部不平坦的二维浅水方程组的组分类

摘要

考虑在不平坦的底部上的二维浅水方程组。获得了用于确定相应对称性的方程组的超定系统。研究了这个超定方程组的兼容性。找到了超定系统解的一般形式。找到对称算子的核。给出了对称算子的核扩展情况。组分类的结果表明，与水平和倾斜底部剖面情况下的一维浅水方程组相比，不平坦底部二维浅水方程组不能通过点变换进行线性化。 。