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Nonlinear self-adjointness of the Krichever-Novikov equation
Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Natural Sciences.
2014 (English)In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, Vol. 19, no 2, 361-363 p.Article in journal (Refereed) Published
Abstract [en]

It is known that the classification of third-order evolutionary equations with the constant separant possessing a nontrivial Lie-Bäcklund algebra (in other words, integrable equations) results in the linear equation, the KdV equation and the Krichever-Novikov equation. The first two of these equations are nonlinearly self-adjoint. This property allows to associate conservation laws of the equations in question with their symmetries. The problem on nonlinear self-adjointness of the Krichever-Novikov equation has not been solved yet. In the present paper we solve this problem and find the explicit form of the differential substitution providing the nonlinear self-adjointness.

Place, publisher, year, edition, pages
Elsevier , 2014. Vol. 19, no 2, 361-363 p.
Keyword [en]
Adjoint equation, Differential substitution, Krichever-Novikov equation, Nonlinear self-adjointness
National Category
Mathematics
Identifiers
URN: urn:nbn:se:bth-6713DOI: 10.1016/j.cnsns.2013.06.011ISI: 000325128700006Local ID: oai:bth.se:forskinfo3DBDC0F8EDC7B144C1257BE80024062EOAI: oai:DiVA.org:bth-6713DiVA: diva2:834246
Available from: 2014-04-23 Created: 2013-09-16 Last updated: 2015-06-30Bibliographically approved

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Ibragimov, Nail
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