Invariant solutions and conservation laws of the generalized Kaup–Boussinesq equation

Abstract

The generalized Kaup–Boussinesq equation is a model which is used to describe the water wave. In this paper, Lie group analysis method is used to perform detailed analysis on the generalized Kaup–Boussinesq equation. Some invariant solutions are obtained under the transformation groups. The conservation laws of the generalized Kaup–Boussinesq equation are constructed using two methods: multiplier method and Ibragimov theorem.

Acknowledgements

Thanks to anonymous referees and editors for their valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Natural Science Foundation of China (NSFC) [grant number 11371287], [grant number 61663043].