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This article is cited in 4 scientific papers (total in 4 papers)
Soliton surfaces in the generalized symmetry approach
A. M. Grundlandab a Centre de Recherches Mathématiques, Université de Montréal, Montréal, Canada
b Département de Mathématiques et d'Informatique Université du Québec à Trois-Rivières, Trois-Rivières, Canada
Abstract:
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, soliton surface, immersion formula,
generalized symmetry.
Received: 26.08.2015 Revised: 06.12.2015
Citation:
A. M. Grundland, “Soliton surfaces in the generalized symmetry approach”, TMF, 188:3 (2016), 416–428; Theoret. and Math. Phys., 188:3 (2016), 1322–1333
Linking options:
https://www.mathnet.ru/eng/tmf9035https://doi.org/10.4213/tmf9035 https://www.mathnet.ru/eng/tmf/v188/i3/p416
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Abstract page: | 390 | Full-text PDF : | 173 | References: | 51 | First page: | 27 |
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