Date: 25 May 2005

Soliton surfaces and their applications (soliton geometry from spectral problems)

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The paper contains a complete presentation of the ideas and results of the approach of soliton surfaces (manifolds). In this approach any n-dim. soliton system with a matrix real semi-simple Lie algebra g possesses its own geometry of n-dim. submanifolds of g. Various applications of this approach are discussed. A particular attention is paid to integrable classical string models.