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Approximate symmetries, conservation laws and numerical solutions for a class of perturbed linear wave type system. (English) Zbl 1427.76197
Summary: The present work considers the Lie group analysis of a system of linear wave type perturbed systems. The methodology is based on finding approximate symmetry operators of a given system. Approximate conservation laws are found via an approximate version of Noether’s theorem. This is based on the modified Noether’s method provided by Ibragimov. Finally a numerical method is applied to solve the considered system.

MSC:
76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
35A30 Geometric theory, characteristics, transformations in context of PDEs
35Q35 PDEs in connection with fluid mechanics
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators
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