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Lie algebras and equations of Korteweg-de Vries type

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Abstract

The survey contains a description of the connection between the infinite-dimensional Lie algebras of Kats-Moody and systems of differential equations generalizing the Korteweg-de Vries and sine-Gordon equations and integrable by the method of the inverse scattering problem. A survey of the theory of Kats-Moody algebras is also given.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki (Noveishie Dostizheniya), Vol. 24, pp. 81–180, 1984.

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Drinfel'd, V.G., Sokolov, V.V. Lie algebras and equations of Korteweg-de Vries type. J Math Sci 30, 1975–2036 (1985). https://doi.org/10.1007/BF02105860

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