On immersion formulas for soliton surfaces

Alfred Michel Grundland, Decio Levi, Luigi Martina

On immersion formulas for soliton surfaces

Číslo: 3/2016
Periodikum: Acta Polytechnica
DOI: 10.14311/AP.2016.56.0180

Klíčová slova: Integrable systems, Soliton surfaces, Immersion formulas, Generalized symmetries, Integrovatelné systémy, povrchy Solitonu, vzorce pro ponoření, generalizované symetrie

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Anotace: This paper is devoted to a study of the connections between three different analytic descriptions for the immersion functions of 2D-surfaces corresponding to the following three types of symmetries: gauge symmetries of the linear spectral problem, conformal transformations in the spectral parameter and generalized symmetries of the associated integrable system. After a brief exposition of the theory of soliton surfaces and of the main tool used to study classical and generalized Lie symmetries, we derive the necessary and sufficient conditions under which the immersion formulas associated with these symmetries are linked by gauge transformations. We illustrate the theoretical results by examples involving the sigma model.