Local Well-Posedness and Orbital Stability of Solitary Wave Solutions for the Generalized Camassa–Holm Equation

ABSTRACT We establish local well-posedness in the Sobolev space H s with any for the generalized Camassa–Holm equation. Furthermore, we consider the stability and instability problem of the solitary wave solutions. Key Words: Camassa–Holm equationLocal well-posednessOrbital stabilitySolitary waves2000 Mathematics Subject Classification: 35B3535G2535Q3576B25 Acknowledgments The authors thank the referee for valuable remarks. Partially supported by Grant MM of MESC and Scientific Research Grant 26/01.04.2004 of Shumen University.