2021-03-05T13:30:41Z
http://oa.upm.es/cgi/oai2
oai:oa.upm.es:11245
2016-04-20T19:23:10Z
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Geometric Integrability of the Camassa-Holm Equation. II
Hernández Heredero, Rafael
Reyes, Enrique G.
Mathematics
Physics
It is known that the Camassa–Holm (CH) equation describes pseudo-spherical surfaces and that therefore its integrability properties can be studied by geometrical means. In particular, the CH equation admits nonlocal symmetries of “pseudo-potential type”: the standard quadratic pseudo-potential associated with the geodesics of the pseudo-spherical surfaces determined by (generic) solutions to CH, allows us to construct a covering π of the equation manifold of CH on which nonlocal symmetries can be explicitly calculated. In this article, we present the Lie algebra of (first-order) nonlocal π-symmetries for the CH equation, and we show that this algebra contains a semidirect sum of the loop algebra over sl(2,R) and the centerless Virasoro algebra. As applications, we compute explicit solutions, we construct a Darboux transformation for the CH equation, and we recover its recursion operator. We also extend our results to the associated Camassa–Holm equation introduced by J. Schiff.
E.U.I.T. Telecomunicación (UPM)
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
2011-07
info:eu-repo/semantics/article
Article
International Mathematics Research Notices, ISSN 1073-7928, 2011-07
PeerReviewed
application/pdf
eng
http://imrn.oxfordjournals.org/content/early/2011/07/10/imrn.rnr120.abstract
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnr120
http://oa.upm.es/11245/