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Stability of Peakons for a Nonlinear Generalization of the Camassa-Holm Equation
  
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KeyWord:Camassa-Holm equation; Peakon; Stability; Heteroclinic cycle; Orbital stability
Author NameAffiliation
Hao Yu Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China 
Kelei Zhang Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China 
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Abstract:
      In this paper, by using the dynamic system method and the known conservation laws of the gCH equation, and underlying features of the peakons, we study the peakon solutions and the orbital stability of the peakons for a nonlinear generalization of the Camassa-Holm equation (gCH). The gCH equation is first transformed into a planar system. Then, by the first integral and algebraic curves of this system, we obtain one heteroclinic cycle, which corresponds to a peakon solution. Moreover, we give a proof of the orbital stability of the peakons for the gCH equation.