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Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete pp 65–76Cite as

RIEMANN-HILBERT PROBLEM AND ALGEBRAIC CURVES

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Part of the book series: NATO Science Series ((NAII,volume 201))

Abstract

There are many problems in pure and applied mathematics that can be solved in terms of a Riemann-Hilbert (R-H problem). The list includes the remarkable class of nonlinear integrable equations, namely nonlinear equations that can be written as the compatibility conditions of linear equations. This class contains a large variety of equations: ODE’s, PDE’s difference equations, etc. Furthermore, the R-H problem formulation provides a powerful technique for obtaining asymptotic results for solutions of ODE’s and PDE’s of this class [1].

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Author information

Authors and Affiliations

  1. Institute of Magnetism NASU, Vernadsky str. 36, Kiev, O3142, Ukraine

    V. Enolskii

  2. International School of Advanced Studies (SISSA), Via Beirut n. 2–4, Trieste, 34014, Italy

    T. Grava

Authors
  1. V. Enolskii
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  2. T. Grava
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Editor information

Editors and Affiliations

  1. Russian Academy of Sciences, St. Petersburg, Russia

    Ludwig Faddeev

  2. Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Pierre Van Moerbeke

  3. Vrije Universiteit Brussel, Belgium

    Franklin Lambert

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Enolskii, V., Grava, T. (2006). RIEMANN-HILBERT PROBLEM AND ALGEBRAIC CURVES. In: Faddeev, L., Van Moerbeke, P., Lambert, F. (eds) Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete. NATO Science Series, vol 201. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-3503-6_7

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