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Algebra i Analiz, 2004, Volume 16, Issue 1, Pages 121–162 (Mi aa592)  

This article is cited in 22 scientific papers (total in 23 papers)

Research Papers

On the Riemann–Hilbert–Birkhoff inverse monodromy problem and the Painlevé equations

A. A. Bolibrucha, A. R. Itsb, A. A. Kapaevc

a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b Department of Mathematical Sciences, Indiana University–Purdue University Indianapolis, Indianapolis, IN, USA
c St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, Russia
References:
Received: 06.10.2003
English version:
St. Petersburg Mathematical Journal, 2005, Volume 16, Issue 1, Pages 105–142
DOI: https://doi.org/10.1090/S1061-0022-04-00845-3
Bibliographic databases:
Document Type: Article
Language: English
Citation: A. A. Bolibruch, A. R. Its, A. A. Kapaev, “On the Riemann–Hilbert–Birkhoff inverse monodromy problem and the Painlevé equations”, Algebra i Analiz, 16:1 (2004), 121–162; St. Petersburg Math. J., 16:1 (2005), 105–142
Citation in format AMSBIB
\Bibitem{BolItsKap04}
\by A.~A.~Bolibruch, A.~R.~Its, A.~A.~Kapaev
\paper On the Riemann--Hilbert--Birkhoff inverse monodromy problem and the Painlev\'e equations
\jour Algebra i Analiz
\yr 2004
\vol 16
\issue 1
\pages 121--162
\mathnet{http://mi.mathnet.ru/aa592}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2069003}
\zmath{https://zbmath.org/?q=an:1077.34089}
\transl
\jour St. Petersburg Math. J.
\yr 2005
\vol 16
\issue 1
\pages 105--142
\crossref{https://doi.org/10.1090/S1061-0022-04-00845-3}
Linking options:
  • https://www.mathnet.ru/eng/aa592
  • https://www.mathnet.ru/eng/aa/v16/i1/p121
    Erratum
    This publication is cited in the following 23 articles:
    1. Bothner T., “On the Origins of Riemann-Hilbert Problems in Mathematics”, Nonlinearity, 34:4 (2021), R1–R73  crossref  mathscinet  isi
    2. A. V. Domrin, B. I. Suleimanov, M. A. Shumkin, “Global Meromorphy of Solutions of the Painlevé Equations and Their Hierarchies”, Proc. Steklov Inst. Math., 311 (2020), 98–113  mathnet  crossref  crossref  mathscinet  isi  elib
    3. Bothner T., Its A., Prokhorov A., “On the Analysis of Incomplete Spectra in Random Matrix Theory Through An Extension of the Jimbo-Miwa-Ueno Differential”, Adv. Math., 345 (2019), 483–551  crossref  mathscinet  zmath  isi  scopus
    4. Hu W., “Singular Asymptotics For Solutions of the Inhomogeneous Painleve II Equation”, Nonlinearity, 32:10 (2019), 3843–3872  crossref  mathscinet  isi
    5. Desiraju H., “The Tau-Function of the Ablowitz-Segur Family of Solutions to Painleve II as a Widom Constant”, J. Math. Phys., 60:11 (2019), 113505  crossref  mathscinet  isi  scopus
    6. Its A.R., Lisovyy O., Prokhorov A., “Monodromy Dependence and Connection Formulae For Isomonodromic Tau Functions”, Duke Math. J., 167:7 (2018), 1347–1432  crossref  mathscinet  zmath  isi  scopus
    7. Bothner T., “Transition asymptotics for the Painlevé II transcendent”, Duke Math. J., 166:2 (2017), 205–324  crossref  mathscinet  zmath  isi  scopus
    8. Guest M.A., Hertling C., “Painlevé III: a Case Study in the Geometry of Meromorphic Connections Preface”: Guest, MA Hertling, C, Painleve III: a Case Study in the Geometry of Meromorphic Connections, Lect. Notes Math., Lecture Notes in Mathematics, 2198, Springer International Publishing Ag, 2017, V+  mathscinet  isi
    9. C. Mitschi, “Some applications of parameterized Picard–Vessiot theory”, Izv. Math., 80:1 (2016), 167–188  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    10. Bothner T., Liechty K., “Tail Decay for the Distribution of the Endpoint of a Directed Polymer”, Nonlinearity, 26:5 (2013), 1449–1472  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. Bothner T., Its A., “The Nonlinear Steepest Descent Approach to the Singular Asymptotics of the Second Painlevé Transcendent”, Physica D, 241:23-24 (2012), 2204–2225  crossref  mathscinet  zmath  adsnasa  isi  scopus
    12. Mitschi C., Singer M.F., “Monodromy Groups of Parameterized Linear Differential Equations with Regular Singularities”, Bull. London Math. Soc., 44:Part 5 (2012), 913–930  crossref  mathscinet  zmath  isi  elib  scopus
    13. Do Y., “A Nonlinear Stationary Phase Method for Oscillatory Riemann–Hilbert Problems”, Int Math Res Not, 2011, no. 12, 2650–2765  mathscinet  zmath  isi  elib
    14. Its A., Niles D., “On the Riemann–Hilbert-Birkhoff Inverse Monodromy Problem Associated with the Third Painlevé Equation”, Lett Math Phys, 96:1–3 (2011), 85–108  crossref  mathscinet  zmath  adsnasa  isi  scopus
    15. Baik J., Buckingham R., DiFranco J., Its A., “Total integrals of global solutions to Painlevé II”, Nonlinearity, 22:5 (2009), 1021–1061  crossref  mathscinet  zmath  adsnasa  isi  scopus
    16. Mityushev V. V., Rogosin S. V., “On the Riemann–Hilbert problem with a piecewise constant matrix”, Z. Anal. Anwend., 27:1 (2008), 53–66  crossref  mathscinet  zmath  isi  elib  scopus
    17. Novokshenov V.Yu., “The Riemann–Hilbert problem and special functions”, Geometric Methods in Physics, AIP Conference Proceedings, 1079, 2008, 149–161  crossref  mathscinet  zmath  adsnasa  isi  scopus
    18. Novokshenov V.Yu., “Connection formulas for the third Painlevé transcendent in the complex plane”, Integrable Systems and Random Matrices: in Honor of Percy Deift, Contemporary Mathematics Series, 458, 2008, 55–69  crossref  mathscinet  zmath  isi
    19. Novokshenov V.Yu., “Asymptotics in the Complex Plane of the Third Painlevé Transcendent”, Difference Equations, Special Functions and Orthogonal Polynomials, 2007, 432–451  crossref  mathscinet  zmath  isi
    20. Sabbah C., “The work of Andrey Bolibrukh on isomonodromic deformations”, Differential Equations and Quantum Groups - ANDREY A. BOLIBRUKH MEMORIAL VOLUME, Irma Lectures in Mathematics and Theoretical Physics, 9, 2007, 9–25  mathscinet  zmath  isi
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