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.
Citation:
V. G. Drinfeld, V. V. Sokolov, “Lie algebras and equations of Korteweg–de Vries type”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 24, VINITI, Moscow, 1984, 81–180; J. Soviet Math., 30:2 (1985), 1975–2036
\Bibitem{DriSok84}
\by V.~G.~Drinfeld, V.~V.~Sokolov
\paper Lie algebras and equations of Korteweg--de~Vries type
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1984
\vol 24
\pages 81--180
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd72}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=760998}
\zmath{https://zbmath.org/?q=an:0578.58040|0558.58027}
\transl
\jour J. Soviet Math.
\yr 1985
\vol 30
\issue 2
\pages 1975--2036
\crossref{https://doi.org/10.1007/BF02105860}
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