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Mat. Sb., 1990, Volume 181, Number 7, Pages 923–933 (Mi msb1201)  

This article is cited in 4 scientific papers (total in 4 papers)

Finite-gap solutions of self-duality equations for $SU(1,1)$ and $SU(2)$ groups and their axisymmetric stationary reductions

D. A. Korotkin

Leningrad Institute of Aviation Instrumentation

Abstract: An extensive new class of solutions is obtained for the $SU(1,1)$ and $SU(2)$ duality equations in terms of the Riemann $\theta$-functions for a Riemann surface depending on the dynamical variables. The dynamics in the resulting solutions is thus determined by the motion of the surface in the moduli manifold. The axisymmetric stationary case is discussed, for which the solutions reduce to solutions of the vacuum Einstein equations. In the degenerate case, the class of solutions is believed to include all known solutions of the instanton and monopole type.

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English version:
Mathematics of the USSR-Sbornik, 1991, 70:2, 355–366

Bibliographic databases:

UDC: 517.43
MSC: Primary 81E13; Secondary 35Q20, 83C05
Received: 25.03.1989

Citation: D. A. Korotkin, “Finite-gap solutions of self-duality equations for $SU(1,1)$ and $SU(2)$ groups and their axisymmetric stationary reductions”, Mat. Sb., 181:7 (1990), 923–933; Math. USSR-Sb., 70:2 (1991), 355–366

Citation in format AMSBIB
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\by D.~A.~Korotkin
\paper Finite-gap solutions of self-duality equations for $SU(1,1)$ and $SU(2)$ groups and their axisymmetric stationary reductions
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\vol 181
\issue 7
\pages 923--933
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\transl
\jour Math. USSR-Sb.
\yr 1991
\vol 70
\issue 2
\pages 355--366
\crossref{https://doi.org/10.1070/SM1991v070n02ABEH001383}
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    Erratum

    This publication is cited in the following articles:
    1. Korotkin D., “Self-Dual Yang-Mills Fields and Deformations of Algebraic-Curves”, Commun. Math. Phys., 134:2 (1990), 397–412  crossref  mathscinet  zmath  adsnasa  isi
    2. Korotkin D., “Algebraic Geometric Solutions of Einstein Equations - Some Physical-Properties”, Commun. Math. Phys., 137:2 (1991), 383–398  crossref  mathscinet  zmath  adsnasa  isi
    3. D. A. Korotkin, “Self-duality equation: Monodromy matrices and algebraic curves”, Journal of Mathematical Sciences (New York), 85:1 (1997), 1684  crossref  mathscinet
    4. A. I. Zenchuk, “Lower-dimensional reductions of GL(M,C) self-dual Yang Mills equation: Solutions with break of wave profiles”, J Math Phys (N Y ), 49:6 (2008), 063502  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник - 1989–1990 Sbornik: Mathematics (from 1967)
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