New travelling wave solutions for a nonlinearly dispersive wave equation of Camassa–Holm equation type

In this paper, the integral bifurcation method is used to study a nonlinearly dispersive wave equation of Camassa–Holm equation type. Loop soliton solution and periodic loop soliton solution, solitary wave solution and solitary cusp wave solution, smooth periodic wave solution and non-smooth periodic wave solution of this equation are obtained, their dynamic characters are discussed. Some solutions have an interesting phenomenon that one solution admits multi-waves when parameters vary.