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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mi mathvariant="normal">Ω</m:mi> </m:math> ${\Omega}$ and the balance index <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mi>σ</m:mi> </m:math> $\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.