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International conference "Geometrical Methods in Mathematical Physics"
December 12, 2011 14:00–14:45, Moscow, Lomonosov Moscow State University
 


Nonlinear self-adjointness and conservation laws

N. Kh. Ibragimovab

a Blekinge Institute of Technology
b Ufa State Aviation Technical University
Video records:
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Flash Video 264.7 Mb
MP4 264.7 Mb
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Adobe PDF 97.3 Kb

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N. Kh. Ibragimov


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Abstract: I introduce the general concept of nonlinear self-adjointness. It embraces author's previous notions of strict self-adjointness and quasi self-adjointness. But the set of nonlinearly self-adjoint equations is essentially wider and includes, in particular, all linear equations. The construction of conservation laws demonstrates a practical significance of the nonlinear self-adjointness. Namely, conservation laws can be associated with symmetries for all nonlinearly self-adjoint systems of differential equations. The system can contain any number of equations. This approach provides a new method for constructing conservation laws and extends Noether's theorem from variational problems to arbitrary systems of differential equations. The new theory is illustrated by various applications.

Materials: gmmp2011_nkhibragimov.pdf (97.3 Kb)

Language: English

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