Potential Conservation Laws

Details Potential Conservation Laws Potential Conservation Laws

2008-03-07

arxiv.org/abs/0803.1156v2

J. Math. Phys. 49 (2008), 103506, 34 pp

Physics

Mathematical Physics

36 pages, extended version

Scientific paper

10.1063/1.2993117

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, Cheviakov and Ivanova [J. Math. Phys., 2006, V.47, 113505]. 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 proved statements is considered. 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.

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