The use of factors to discover potential systems or linearizations. (English) Zbl 0841.35005
A conservation law of a PDE system is named a potential conservation law if at least one component of its generating function is a nowhere vanishing function. It is shown that every potential conservation law generates the covering PDE system of the initial system and that point symmetries of this covering can yield nonlocal symmetries of the initial system and its linearization by a differential substitution. Necessary conditions for the existence of a linearization of a PDE system are given.
Reviewer: V.A.Yumaguzhin (Pereslavl’-Zalesskij)
MSC:
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 58J70 | Invariance and symmetry properties for PDEs on manifolds |
| 35K55 | Nonlinear parabolic equations |
| 22E65 | Infinite-dimensional Lie groups and their Lie algebras: general properties |
| 58B25 | Group structures and generalizations on infinite-dimensional manifolds |
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