The method of Lie symmetry analysis of differential equations is applied to determine exact solutions for the Camassa–Choi equation and its generalization. We prove that the Camassa–Choi equation is invariant under an infinity-dimensional Lie algebra, with an essential five-dimensional Lie algebra. The application of the Lie point symmetries leads to the construction of exact similarity solutions.

中文翻译：

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Camassa–Choi方程的李对称性分析和相似解

应用微分方程的Lie对称分析方法确定Camassa–Choi方程的精确解及其推广。我们证明了在无穷维李代数与基本五维李代数下，Camassa-Choi方程是不变的。Lie点对称性的应用导致了精确相似性解的构造。