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arXiv · 1109.1719

Conservation laws and symmetries of quasilinear radial wave equations in multi-dimensions

Stephen C. Anco·Steven A. MacNaughton·Thomas Wolf
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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 of Morawetz dilation identity that produces conservation laws for each of the two wave equations in a different way than Noether's theorem.

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Stephen C. Anco, Steven A. MacNaughton, Thomas Wolf. 2014-05-19. Conservation laws and symmetries of quasilinear radial wave equations in multi-dimensions. https://doi.org/10.1063/1.4711814

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