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Please use this identifier to cite or link to this item: http://dspace.utalca.cl/handle/1950/8961

Title: The Modified Camassa-Holm Equation
Authors: Gorka, P.
Reyes, E.G.
Issue Date: 2011
Abstract: The Camassa-Holm (CH) equation describes pseudo-spherical surfaces and therefore its integrability properties can be studied by geometrical means [Reyes, "Geometric integrability of the Camassa-Holm equation." Letters in Mathematical Physics 59 (2002): 117-31]. Using this fact, we introduce a "Miura transform" and a "modified" Camassa-Holm (mCH) equation, in analogy with the Korteweg-de Vries theory. We obtain an infinite number of local conservation laws for CH from these data and also an infinite number of (non)local symmetries. We then compute conservation laws for mCH and also show that it describes pseudo-spherical surfaces, so that, in particular, it is the integrability condition of an <inline-graphic xlink:href="RNQ163IM1" xmlns:xlink="http://www.w3.org/1999/xlink"/>-valued linear problem. Finally, we investigate mCH analytically: we define weak solutions and prove their existence and uniqueness.
Description: Gorka, P (Gorka, Przemyslaw). Univ Talca, Inst Matemat & Fis, Talca, Chile . Warsaw Univ Technol, Dept Math & Informat Sci, PL-00661 Warsaw, Poland
URI: http://dspace.utalca.cl/handle/1950/8961
Appears in Collections:Artículos en publicaciones ISI - Universidad de Talca

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