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Symmetries and conservation laws of the generalized Krichever-Novikov equation
Brock Univ, Dept Math & Stat, St Catharines, ON L2S 3A1, Canada..
Ufa State Aviat Tech Univ, Lab Grp Anal Math Models Nat & Engn Sci, Ufa 450000, Russia..
Ufa State Aviat Tech Univ, Lab Grp Anal Math Models Nat & Engn Sci, Ufa 450000, Russia..
Ufa State Aviat Tech Univ, Lab Grp Anal Math Models Nat & Engn Sci, Ufa 450000, Russia..
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2016 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 49, no 10, 105201Article in journal (Refereed) PublishedText
Abstract [en]

A computational classification of contact symmetries and higher-order local symmetries that do not commute with t, x, as well as local conserved densities that are not invariant under t, x is carried out for a generalized version of the Krichever-Novikov (KN) equation. Several new results are obtained. First, the KN equation is explicitly shown to have a local conserved density that contains t, x. Second, apart from the dilational point symmetries known for special cases of the KN equation and its generalized version, no other local symmetries with low differential order are found to contain t, x. Third, the basic Hamiltonian structure of the KN equation is used to map the local conserved density containing t, x into a nonlocal symmetry that contains t, x. Fourth, a recursion operator is applied to this nonlocal symmetry to produce a hierarchy of nonlocal symmetries that have explicit dependence on t, x. When the inverse of the Hamiltonian map is applied to this hierarchy, only trivial conserved densities are obtained.

Place, publisher, year, edition, pages
2016. Vol. 49, no 10, 105201
Keyword [en]
integrable system, conservation law, symmetry, Krichever-Novikov equation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:bth-11660DOI: 10.1088/1751-8113/49/10/105201ISI: 000369256700007OAI: oai:DiVA.org:bth-11660DiVA: diva2:908303
Available from: 2016-03-02 Created: 2016-02-29 Last updated: 2016-03-03Bibliographically approved

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Ibragimov, Nail
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Department of Mathematics and Natural Sciences
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