×

zbMATH — the first resource for mathematics

Breakdown of the Camassa-Holm equation. (English) Zbl 1052.35130
This is a brief note that deals with the breakdown of the Camassa-Holm equation. An earlier proof regarding the breakdown of this equation, under certain conditions, is pointed out to be faulty at some point; a simple proof dropping some conditions, assumed earlier, is presented, of course using the same formalism.

MSC:
35F20 Nonlinear first-order PDEs
35B40 Asymptotic behavior of solutions to PDEs
35L67 Shocks and singularities for hyperbolic equations
35Q58 Other completely integrable PDE (MSC2000)
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
Keywords:
shock wave
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] ; Vorticity and incompressible flow. Cambridge University Press, Cambridge, 2002. · Zbl 0983.76001
[2] Camassa, Phys Rev Lett 71 pp 1661– (1993)
[3] Camassa, Adv Appl Math 31 pp 1– (1994)
[4] McKean, Asian J Math 2 pp 767– (1998) · Zbl 0959.35140
[5] McKean, Asian J Math 3 (1999)
[6] McKean, Comm Pure Appl Math 61 pp 638– (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.