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New Peakons and Periodic Peakons of the Modified Camassa-Holm Equation
  
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KeyWord:Camassa-Holm equation; Peakon; Periodic peakon; Solitary wave; Periodic wave
Author NameAffiliation
Xinhui Lu School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China 
Lin Lu Department of Mathematics, Hunan First Normal University, Changsha, Hunan 410205, China 
Aiyong Chen School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China
Department of Mathematics, Hunan First Normal University, Changsha, Hunan 410205, China 
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Abstract:
      In this paper, we obtain new peakon and periodic peakon solutions to a modified Camassa-Holm equation. We change the modified Camassa- Holm equation into a planar system. Then the first integral and algebraic curves of this system are obtained. By using the first integral and algebraic curves, a new peakon solution is given by hyperbolic function. Moreover, some new periodic peakons are given by elliptic functions and triangle functions.