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Mat. Zametki, 2016, Volume 100, Issue 6, Pages 868–880 (Mi mz11360)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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.


DOI: https://doi.org/10.4213/mzm11360

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English version:
Mathematical Notes, 2016, 100:6, 835–846

Bibliographic databases:

UDC: 514.76+517.95
Received: 29.08.2016

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. G. Novikov, I. A. Taimanov, “Darboux–Moutard transformations and Poincaré–Steklov operators”, Proc. Steklov Inst. Math., 302 (2018), 315–324  mathnet  crossref  crossref  isi  elib
  • Математические заметки Mathematical Notes
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