Jiangbo Zhou, Lu Yao, Lixin Tian, Wenbin Zhang
Published 2013-04-26, updated 2013-05-01Version 2
In this paper, we investigate the orbital stability problem of peakons for a modified Camassa-Holm equation with both quadratic and cubic nonlinearity. This equation was derived from integrable theory and admits peaked soliton (peakon) and multipeakon solutions. By constructing two suitable piecewise functions, we establish the polynomial inequality relating to two conserved quantities and the maximum of the solution to this equation. The error estimate between the maximum of the solution and the peakon then follows from the structure of the polynomial inequality. Finally, we prove that a wave starting close to the peakon remains close to some translate of it at all later times, that is, the shapes of these peakons are stable under small perturbations.
Comments: Since the same result is already contained in the paper written by Changzheng Qu et al, this paper has been withdrawn by the authors. Many thanks for Prof. Qu's email
On the Cauchy problem for a generalized Camassa-Holm equation with both quadratic and cubic nonlinearity
Spectral stability of multiple periodic waves for the Schrodinger system with cubic nonlinearity
Spectral instability of peakons for the $b$-family of Novikov equations
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