Potential conservation laws
- Fakultaet fuer Mathematik, Universitaet Wien, Nordbergstrasse 15, A-1090 Wien (Austria)
We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially depend on potential variables. This statement provides a significant generalization of results of the recent paper by Bluman et al. [J. Math. Phys. 47, 113505 (2006)]. Moreover, we present extensions to gauged potential systems, Abelian and general coverings, and general foliated systems of differential equations. An example illustrating possible applications of these results is given. A special version of the Hadamard lemma for fiber bundles and the notions of weighted jet spaces are proposed as new tools for the investigation of potential conservation laws.
- OSTI ID:
- 21175674
- Journal Information:
- Journal of Mathematical Physics, Vol. 49, Issue 10; Other Information: DOI: 10.1063/1.2993117; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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