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Lie algebras and equations of Korteweg–de Vries type

V. G. Drinfeld, V. V. Sokolov


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.

UDC: 515.168.3+517.957

 English version: Journal of Soviet Mathematics, 1985, 30:2, 1975–2036

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