Nonlinear self-adjointness of the Krichever-Novikov equation

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Adjoint equation

Differential substitution

Krichever-Novikov equation

Nonlinear self-adjointness

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