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Relationship between symmetries and conservation laws. (English) Zbl 0962.35009
The article discusses the relation between Lie-Bäcklund symmetries and conservation laws for arbitrary differential equations, i.e. it is not assumed that the equation comes from a variational principle as in the classical Noether theorem. An equation relating the symmetry generator and the components of a conservation law invariant under it is derived. This equation is applied to derive conservation laws for several classical equations in mathematical physics.

MSC:
35A30 Geometric theory, characteristics, transformations in context of PDEs
58J72 Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds
35Q53 KdV equations (Korteweg-de Vries equations)
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