Lie symmetry analysis and similarity solutions for the Camassa-Choi equations

TL;DR

This paper applies Lie symmetry analysis to the Camassa-Choi equation, revealing its invariance under an infinite-dimensional algebra and deriving exact similarity solutions, advancing understanding of its mathematical structure.

Contribution

It introduces a comprehensive Lie symmetry analysis for the Camassa-Choi equation and constructs explicit similarity solutions, highlighting its symmetry properties.

Findings

Camassa-Choi equation is invariant under an infinite-dimensional Lie algebra

Identification of a five-dimensional Lie algebra structure

Derivation of exact similarity solutions

Abstract

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 infinite-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.