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Perturbation methods in group analysis

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Abstract

In this paper we describe the theory of approximate groups of transformations which lets us constructively find approximate symmetries of equations with a small parameter. For evolution equations we introduce the concept of formal symmetries and Bäcklund transformations. The theory is applied to a large class of wave and evolution equations.

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Authors
  1. V. A. Baikov
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  2. R. K. Gazizov
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  3. N. Kh. Ibragimov
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Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 34, pp. 85–147, 1989.

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Baikov, V.A., Gazizov, R.K. & Ibragimov, N.K. Perturbation methods in group analysis. J Math Sci 55, 1450–1490 (1991). https://doi.org/10.1007/BF01097534

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  • DOI: https://doi.org/10.1007/BF01097534

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