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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 188, Number 3, Pages 416–428
DOI: https://doi.org/10.4213/tmf9035
(Mi tmf9035)
 

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
Full-text PDF (435 kB) Citations (4)
References:
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.
Funding agency Grant number
Natural Sciences and Engineering Research Council of Canada (NSERC)
This research was supported by a research grant of the NSERC of Canada.
Received: 26.08.2015
Revised: 06.12.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 188, Issue 3, Pages 1322–1333
DOI: https://doi.org/10.1134/S004057791609004X
Bibliographic databases:
PACS: 02.20Sv, 02.30Ik, 02.40Dr
MSC: 35Q53, 35Q58, 53A05
Language: Russian
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
Citation in format AMSBIB
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:51
    First page:27
     
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