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International conference "Geometrical Methods in Mathematical Physics"
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Nonlinear self-adjointness and conservation laws N. Kh. Ibragimovab a Blekinge Institute of Technology b Ufa State Aviation Technical University |
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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. Language: English |
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