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 Noetherâs theorem for each of the two wave equations.