On the relation between weak and strong invariance of differential equations |
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| Authors: | José F. Cariñena M. A. Del Olmo P. Winternitz |
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| Affiliation: | (1) Departamento de Fisica Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain;(2) Departamento de Fisica Teórica, Universidad de Valladolid, 47011 Valladolid, Spain;(3) Centre de Recherches Mathematiques, Université de Montréal, CP 6128-A, H3C 3J7 Montréal, Quebec, Canada |
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| Abstract: | Some concepts of Lie algebra cohomology are used to systematize the search for differential equations invariant under a given Lie groupG. In particular, it is shown that if a  strongly invariant equation exists, then all weakly invariant equations differ from it only by an arbitrary multiplicative factor. If no strongly invariant equation exists, then cohomology theory can be used to simplify the search for weakly invariant equations. |
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| Keywords: | 17B56 57T10 22Exx |
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