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

Please always quote using this URN: urn:nbn:de:0297-zib-16111
  • 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 classes of wave equations in a different way than Noether's theorem.

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Author:Stephen S. Anco, Steven A. MacNaughton, Thomas Wolf
Document Type:ZIB-Report
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
70-XX MECHANICS OF PARTICLES AND SYSTEMS (For relativistic mechanics, see 83A05 and 83C10; for statistical mechanics, see 82-XX)
Date of first Publication:2012/10/17
Series (Serial Number):ZIB-Report (12-33)
ArXiv Id:http://arxiv.org/abs/1109.1719
ISSN:1438-0064
Published in:Appeared in: Journal of Mathematical Physics (2012), Volume 53, Issue 5, 33 pages
DOI:https://doi.org/10.1063/1.4711814