A. M. Grundland, S. Post, D. Riglioni
This communication presents a detailed description of the symmetries of integrable systems which are used to construct the Fokas-Gel'fand formula for immersion of 2D-soliton surfaces, associated with such systems, into Lie algebras. In addition, it contains an exposition of the main tool used to study symmetries of these systems, which allows us to find the explicit integrated form of the surfaces. We determine that the sufficient condition for the applicability of the Fokas-Gel'fand immersion formula of a 2D-surface is that the vector field be a common symmetry of an integrable system and its linear spectral problem.
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http://arxiv.org/abs/1302.6887
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