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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.

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