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Approximate Noether-type symmetries and conservation laws via partial Lagrangians for PDEs with a small parameter. (English) Zbl 1158.35306
Summary: We show how one can construct approximate conservation laws of approximate Euler-type equations via approximate Noether-type symmetry operators associated with partial Lagrangians. The ideas of the procedure for a system of unperturbed partial differential equations are extended to a system of perturbed or approximate partial differential equations. These approximate Noether-type symmetry operators do not form a Lie algebra in general. The theory is applied to the perturbed linear and nonlinear \((1+1)\) wave equations and the Maxwellian tails equation. We have also obtained new approximate conservation laws for these equations.

35A30 Geometric theory, characteristics, transformations in context of PDEs
58J70 Invariance and symmetry properties for PDEs on manifolds
Full Text: DOI
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