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Zbl 1049.35149
Constantin, Adrian; Strauss, Walter A.
Stability of peakons. (English)
[J] Commun. Pure Appl. Math. 53, No. 5, 603-610 (2000). ISSN 0010-3640

The authors prove the orbital stability of peakon solutions of the Camassa-Holm equation in the $H^1$ norm under the assumption of their existence. The proof is based on estimates for two conservation laws of the equation. Some comments on known results concerning the well-posedness of the initial value problem and the existence of solutions conclude the article.
[Werner M. Seiler (Heidelberg)]

MSC 2000:: *35Q53 KdV-like equations
35Q51 Solitons
37K45 Stability problems
35B35 Stability of solutions of PDE
76B15 Wave motions (fluid mechanics)

Keywords: Camassa-Holm equation; soliton; peakon; orbital stability

Cited in: Zbl 1180.35453 Zbl 1171.35459

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