Stability of Negative Solitary Waves for a Generalized Camassa-Holm Equation with Quartic Nonlinearity

Abstract

We consider the stability of negative solitary waves to a generalized Camassa-Holm equation with quartic nonlinearity. We obtain the existence of negative solitary waves for any wave speedc>0and some of their qualitative properties and then prove that they are orbitally stable by using a method proposed by Grillakis et al.