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Publication: Conservation Laws and Symmetries of Quasilinear Wave Equations in multi-dimensions I: Radial formulation

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Title Conservation Laws and Symmetries of Quasilinear Wave Equations in multi-dimensions I: Radial formulation
Authors/Editors* S C Anco, S MacNaughton, T Wolf
Where published* preprint
How published* Other
Year* 2011
Volume
Number
Pages 37
Publisher
Keywords wave equations, symmetries, conservation laws
Link http://lie.math.brocku.ca/twolf/papers/AMW11.pdf
Abstract
Abstract. Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of point type and all conservation laws of a general energy-momentum type are explicitly determined, including those such as dilations, inversions, similarity energies and conformal energies that exist only for special powers or dimensions. In particular, all variational cases (when a Lagrangian formulation exists) and non-variational cases (when no Lagrangian exists) for these wave equations are considered. As main results, the classification yields generalized energies and radial momenta in certain non-variational cases, which are shown to arise from a new type ofMorawetz dilation identity that produces conservation laws in a different way than Noether’s theorem for each of the two wave equations.
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