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Matematicheskie Zametki, 2016, Volume 100, Issue 6, Pages 868–880
DOI: https://doi.org/10.4213/mzm11360 (Mi mzm11360) 		 
This article is cited in 7 scientific papers (total in 7 papers)

The Moutard Transformation of Two-Dimensional Dirac Operators and the Conformal Geometry of Surfaces in Four-Dimensional Space

R. M. Matueva, I. A. Taimanovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (507 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm11360
Abstract: The Moutard transformation for the two-dimensional Dirac operator with complex-valued potential is constructed. It is shown that this transformation binds the potentials of Weierstrass representations of the surfaces related by the composition of inversion and reflection with respect to the axis. An explicit analytic example of a transformation leading to the appearance of double points on the spectral curve of the Dirac operator is described analytically.
Keywords: two-dimensional Dirac operator, Moutard transformation, Weierstrass representation, inversion, Floquet functions, spectral curve.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan 3485/ГФ4
This work was supported by the Ministry of Education and Science of the Republic of Kazakhstan under grant 3485/GF4.
Received: 29.08.2016
English version:
Mathematical Notes, 2016, Volume 100, Issue 6, Pages 835–846
DOI: https://doi.org/10.1134/S0001434616110237
Bibliographic databases:
Document Type: Article
UDC: 514.76+517.95
Language: Russian
Citation: R. M. Matuev, I. A. Taimanov, “The Moutard Transformation of Two-Dimensional Dirac Operators and the Conformal Geometry of Surfaces in Four-Dimensional Space”, Mat. Zametki, 100:6 (2016), 868–880; Math. Notes, 100:6 (2016), 835–846
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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