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.


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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