Symmetry analysis and explicit power series solutions of the Boussinesq–Whitham–Broer–Kaup equation

Abstract

This paper focus on two aspects. Firstly, symmetry analysis is performed for the Boussinesq–Whitham–Broer–Kaup equation which can degenerate to the Boussinesq equation, the Whitham–Broer–Kaup equation and the Broer–Kaup equation. As a byproduct, the similarity reductions and exact solutions of the equation are constructed based on the optimal systems. Secondly, the explicit solutions are considered by the power series method. Moreover, the convergence of the power series solutions are shown. The physical significance of the solutions is considered from the transformation group point of view.