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.
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