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Nonlocal trends in the geometry of differential equations: Symmetries, conservation laws, and Bäcklund transformations

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Abstract

The theory of coverings over differential equations is exposed which is an adequate language for describing various nonlocal phenomena: nonlocal symmetries and conservation laws, Bäcklund transformations, prolongation structures, etc. A notion of a nonlocal cobweb is introduced which seems quite useful for dealing with nonlocal objects.

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Krasil'shchik, I.S., Vinogradov, A.M. Nonlocal trends in the geometry of differential equations: Symmetries, conservation laws, and Bäcklund transformations. Acta Appl Math 15, 161–209 (1989). https://doi.org/10.1007/BF00131935

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