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

被引：7
|
作者：
Matuev, R. M. [1 ,2 ]
Taimanov, I. A. [1 ,2 ]
机构：
[1] Russian Acad Sci, Sobolev Inst Math, Siberian Branch, Novosibirsk, Russia
[2] Novosibirsk Natl Res State Univ, Novosibirsk, Russia
来源：
MATHEMATICAL NOTES | 2016年 / 100卷 / 5-6期
关键词：
two-dimensional Dirac operator; Moutard transformation; Weierstrass representation; inversion; Floquet functions; spectral curve;
D O I：
10.1134/S0001434616110237
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：835 / 846
页数：12
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