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Nonlinear self-adjointness of the Krichever-Novikov equation
- Galiakberova, L. R. (author)
-
- Ibragimov, Nail (author)
- Blekinge Tekniska Högskola,Avdelningen för matematik och naturvetenskap
- (creator_code:org_t)
- Elsevier, 2014
- 2014
- English.
- In: Communications in nonlinear science & numerical simulation. - : Elsevier. - 1007-5704 .- 1878-7274. ; 19:2, s. 361-363
- Journal article (peer-reviewed)
Abstract
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- Adjoint equation
- Differential substitution
- Krichever-Novikov equation
- Nonlinear self-adjointness
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- ref (subject category)
- art (subject category)
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