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Transformation groups in net spaces

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Abstract

We consider formal groups of transformations on the space of differential and net (finite-difference) variables. We show that preservation of meaning of difference derivatives under transformations necessarily leads to Lie-Bäcklund group. We derive formulas for extension to net variables and formulate criteria for preservation of uniformity and invariance of differences of the network and a test for the invariance of difference equations. With the help of formal Newton series we construct the ideal of the algebra of all Lie-Bäcklund operators on a uniform network which is used to derive tests for the conservatism of difference equations on the basis of a discrete analog of Noether's identity.

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Authors
  1. V. A. Dorodnitsyn
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Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 34, pp. 149–191, 1989.

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Dorodnitsyn, V.A. Transformation groups in net spaces. J Math Sci 55, 1490–1517 (1991). https://doi.org/10.1007/BF01097535

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  • DOI: https://doi.org/10.1007/BF01097535

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