Potential Conservation Laws
arXiv:0803.1156 · doi:10.1063/1.2993117
Abstract
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.
36 pages, extended version
References in corpus (6)
- Conservation Laws and Potential Symmetries of Linear Parabolic Equations
- Hierarchy of Conservation Laws of Diffusion--Convection Equations
- Potential equivalence transformations for nonlinear diffusion-convection equations
- On recursion operators and nonlocal symmetries of evolution equations
- Reducibility of zero curvature representations with application to recursion operators
- Conservation Laws of Variable Coefficient Diffusion-Convection Equations
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