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Self-adjointness of a generalized Camassa-Holm equation
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
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2011 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 218, no 6, 2579-2583 p.Article in journal (Refereed) Published
Abstract [en]

It is well known that the Camassa-Holm equation possesses numerous remarkable properties characteristic for KdV type equations. In this paper we show that it shares one more property with the KdV equation. Namely, it is shown in [1,2] that the KdV and the modified KdV equations are self-adjoint. Starting from the generalization [3] of the Camassa-Holm equation [4], we prove that the Camassa-Holm equation is self-adjoint. This property is important, e.g. for constructing conservation laws associated with symmetries of the equation in question. Accordingly, we construct conservation laws for the generalized Camassa-Holm equation using its symmetries.

Place, publisher, year, edition, pages
Elsevier , 2011. Vol. 218, no 6, 2579-2583 p.
Keyword [en]
Camassa-Holm equation, Conservation laws, Quasi self-adjointness
National Category
Mathematics
Identifiers
URN: urn:nbn:se:bth-7381DOI: 10.1016/j.amc.2011.07.074ISI: 000296278800020Local ID: oai:bth.se:forskinfo26624310AEF85400C1257979002F654BOAI: oai:DiVA.org:bth-7381DiVA: diva2:834989
Available from: 2012-09-18 Created: 2012-01-02 Last updated: 2015-09-28Bibliographically approved

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Ibragimov, Nail H.Khamitova, Raisa
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