Solitary waves of the degenerate rotation-two-component Camassa–Holm system

Abstract Considered herein are the classification of solitary wave solutions of the degenerate rotation-two-component Camassa–Holm system. Depending on the values of the rotating parameter Ω ${\Omega}$ and the balance index σ $\sigma $ , we classify various localized solitary wave solutions (smooth, peakons, and cuspons) for this model. We also prove that horizontally symmetric weak solution of this model must be traveling waves.