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Funktsional. Anal. i Prilozhen.:

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Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 4, Pages 18–34 (Mi faa323)  

This article is cited in 12 scientific papers (total in 12 papers)

Theta Function Solutions of the Schlesinger System and the Ernst Equation

D. A. Korotkina, V. B. Matveevb

a Concordia University, Department of Mathematics and Statistics
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: We establish a link between the Schlesinger system and the Ernst equation (the stationary axisymmetric Einstein equation) on the level of algebro-geometric solutions. We calculate all metric coefficients corresponding to general algebro-geometric solutions of the Ernst equation.


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English version:
Functional Analysis and Its Applications, 2000, 34:4, 252–264

Bibliographic databases:

UDC: 517.9
Received: 26.04.1999

Citation: D. A. Korotkin, V. B. Matveev, “Theta Function Solutions of the Schlesinger System and the Ernst Equation”, Funktsional. Anal. i Prilozhen., 34:4 (2000), 18–34; Funct. Anal. Appl., 34:4 (2000), 252–264

Citation in format AMSBIB
\by D.~A.~Korotkin, V.~B.~Matveev
\paper Theta Function Solutions of the Schlesinger System and the Ernst Equation
\jour Funktsional. Anal. i Prilozhen.
\yr 2000
\vol 34
\issue 4
\pages 18--34
\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 4
\pages 252--264

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    This publication is cited in the following articles:
    1. Frauendiener J., Klein C., “Exact relativistic treatment of stationary counterrotating dust disks: Physical properties”, Physical Review D, 63:8 (2001), 084025  crossref  mathscinet  adsnasa  isi
    2. Klein C., “Exact relativistic treatment of stationary counterrotating dust disks: Boundary value problems and solutions”, Physical Review D, 63:6 (2001), 064033  crossref  mathscinet  adsnasa  isi
    3. Klein, C, “Ernst equation, Fay identities and variational formulas on hyperelliptic curves”, Mathematical Research Letters, 9:1 (2002), 27  crossref  mathscinet  zmath  isi  scopus
    4. C. Klein, “Isomonodromy Approach to Boundary Value Problems for the Ernst Equation”, Theoret. and Math. Phys., 134:1 (2003), 72–85  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. C. Klein, “The Kerr Solution on Partially Degenerate Hyperelliptic Riemann Surfaces”, Theoret. and Math. Phys., 137:2 (2003), 1520–1526  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Klein, C, “On explicit solutions to the stationary axisymmetric Einstein-Maxwell equations describing dust disks”, Annalen der Physik, 12:10 (2003), 599  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Klein, C, “Exact relativistic treatment of stationary black-hole-disk systems”, Physical Review D, 68:2 (2003), 027501  crossref  mathscinet  adsnasa  isi  scopus
    8. Karas, V, “Gravitating discs around black holes”, Classical and Quantum Gravity, 21:7 (2004), R1  crossref  mathscinet  zmath  adsnasa  isi  scopus
    9. Katsnelson V., Volok D., “Rational solutions of the Schlesinger system and isoprincipal deformations of rational matrix functions I”, Current Trends in Operator Theory and its Applications, Operator Theory : Advances and Applications, 149, 2004, 291–348  mathscinet  zmath  isi
    10. Matveev, VB, “30 years of finite-gap integration theory”, Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 366:1867 (2008), 837  crossref  mathscinet  zmath  adsnasa  isi  scopus
    11. Lenells J., “Boundary Value Problems for the Stationary Axisymmetric Einstein Equations: A Disk Rotating Around a Black Hole”, Comm Math Phys, 304:3 (2011), 585–635  crossref  mathscinet  zmath  adsnasa  isi  scopus
    12. Brezhnev Yu.V., “Spectral/Quadrature Duality: Picard-Vessiot Theory and Finite-Gap Potentials”, Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, Contemporary Mathematics, 563, ed. AcostaHumanez P. Finkel F. Kamran N. Olver P., Amer Mathematical Soc, 2012, 1–31  crossref  mathscinet  zmath  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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