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Zbl 1079.53075
Grahovski, Georgi G.; Gerdjikov, Vladimir S.; Kostov, Nikolay A.
On the multi-component NLS type equations on symmetric spaces: reductions and soliton solutions. (English)
[A] Mladenov, Iva\"ilo M.(ed.) et al., Proceedings of the 6th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 3--10, 2004. Sofia: Bulgarian Academy of Sciences. 203-217 (2005). ISBN 954-84952-9-5/pbk

This is an introductory survey on multi-component nonlinear Schrödinger equations related to simple Lie algebras and symmetric spaces. These generalizations of the nonlinear Schrödinger equation were proposed by Fordy and Kulish in the early 1990's. Recently, the authors sytematically studied these equations, their reductions and soliton solutions [Inverse Probl. 17, No. 4, 999--1015 (2001; Zbl 0988.35143) and J. Phys. A, Math. Gen. 34, No. 44, 9425--9461 (2001; Zbl 1001.37074)]. In particular, some of their results on this subject are reviewed and discussed in this paper.
[Iskander A. Taimanov (Novosibirsk)]

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
37K10 Completely integrable systems etc.
37K30 Relations with algebraic structures
53C35 Symmetric spaces (differential geometry)
35Q51 Solitons

Keywords: soliton equations; nonlinear Schrödinger equation; symmetric spaces

Citations: Zbl 0988.35143; Zbl 1001.37074

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	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

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