Classification and Traveling Wave Solutions for the Gilson–Pickering Equation

Abstract

The main purpose of this paper is to form a complete group classification for the Gilson–Pickering equation. Exact traveling wave solutions and bifurcations of the Gilson–Pickering equation are studied by the method of dynamical systems. The study on the wave solutions of the model derives a planar Hamiltonian system. Based on phase portraits, many exact explicit parametric representations of wave solutions are obtained under different parametric conditions.