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Lie symmetry analysis and similarity solutions for the Camassa-Choi equations. (English) Zbl 1456.35166

Summary: 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.

MSC:

35Q35 PDEs in connection with fluid mechanics
17B30 Solvable, nilpotent (super)algebras
35A30 Geometric theory, characteristics, transformations in context of PDEs
35B06 Symmetries, invariants, etc. in context of PDEs

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