English

Stability of peakons for the Degasperis-Procesi equation

Analysis of PDEs 2007-12-13 v1 Mathematical Physics math.MP

Abstract

The Degasperis-Procesi equation can be derived as a member of a one-parameter family of asymptotic shallow water approximations to the Euler equations with the same asymptotic accuracy as that of the Camassa-Holm equation. In this paper, we study the orbital stability problem of the peaked solitons to the Degasperis-Procesi equation on the line. By constructing a Liapunov function, we prove that the shapes of these peakon solitons are stable under small perturbations.

Keywords

Cite

@article{arxiv.0712.2007,
  title  = {Stability of peakons for the Degasperis-Procesi equation},
  author = {Zhiwu Lin and Yue Liu},
  journal= {arXiv preprint arXiv:0712.2007},
  year   = {2007}
}

Comments

21 pages, to appear in Comm. Pure Appl. Math