Geodesic
Soliton surfaces in the generalized symmetry approach
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 3, pp. 416-428 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate some features of generalized symmetries of integrable systems aiming to obtain the Fokas–Gel'fand formula for the immersion of two-dimensional soliton surfaces in Lie algebras. We show that if there exists a common symmetry of the zero-curvature representation of an integrable partial differential equation and its linear spectral problem, then the Fokas–Gel'fand immersion formula is applicable in its original form. In the general case, we show that when the symmetry of the zero-curvature representation is not a symmetry of its linear spectral problem, then the immersion function of the two-dimensional surface is determined by an extended formula involving additional terms in the expression for the tangent vectors. We illustrate these results with examples including the elliptic ordinary differential equation and the $\mathbb{C}P^{N-1}$ sigma-model equation.
Keywords: integrable system, generalized symmetry.
Mots-clés : soliton surface, immersion formula 
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A. M. Grundland. Soliton surfaces in the generalized symmetry approach. Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 3, pp. 416-428. http://geodesic.mathdoc.fr/item/TMF_2016_188_3_a3/

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