The Moutard transformation of two-dimensional Dirac operators and the conformal geometry of surfaces in four-dimensional space

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• 作者：R. M. Matuev ; I. A. Taimanov
• 关键词：two ; dimensional Dirac operator ; Moutard transformation ; Weierstrass representation ; inversion ; Floquet functions ; spectral curve
• 刊名：Mathematical Notes
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：100
• 期：5-6
• 页码：835-846
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Pleiades Publishing
• ISSN：1573-8876
• 卷排序：100

文摘

The Moutard transformation for the two-dimensional Dirac operator with complexvalued 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.