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A basis of approximate conservation laws for PDEs with a small parameter. (English) Zbl 1160.35318
Summary: The generation of new approximate conservation laws by the action of approximate Lie-Bäcklund symmetry generators on known conservation laws for a given system of perturbed or approximate partial differential equations is studied. The ideas of the classical generation theorem of conservation laws from known ones by the action of any Lie-Bäcklund symmetry generator of a given system of unperturbed partial differential equations are extended to a system of perturbed partial differential equations. We show that the generated approximate conservation laws are non-trivial if the system of the perturbed partial differential equations is derivable from a variational principle. We also determine a basis of approximate conservation laws for a given system of perturbed partial differential equations. Applications are made to perturbed linear and non-linear (1+1) wave equations.

MSC:
35A30 Geometric theory, characteristics, transformations in context of PDEs
35B20 Perturbations in context of PDEs
35L65 Hyperbolic conservation laws
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