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The Painlevé III equation and the Iwasawa decomposition

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Abstract

For the third Painlevé equation an explicit isomorphism between the monodromy data and the data of the approach of Dorfmeister-Pedit-Wu, based on the Iwasawa decomposition of the loop groups, is established. As an application, this provides a simple algebraic way to calculate the monodromy data in terms of the Cauchy data at zero.

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Authors and Affiliations

  1. FB Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, 10623, Berlin, Gernany

    Alexander Bobenko & Alexander Its

  2. Dept. of Mathematical Sciences, Indiana University-Purdue University at Indianapolis, 402 N Blackford Street, 46202-3216, Indianapolis, IN, USA

    Alexander Bobenko & Alexander Its

Authors
  1. Alexander Bobenko
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  2. Alexander Its
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Partially supported by the Sonderforschungsbereich 288

Partially supported by the National Science Foundation (DMS-9315964)

This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag.

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Bobenko, A., Its, A. The Painlevé III equation and the Iwasawa decomposition. Manuscripta Math 87, 369–377 (1995). https://doi.org/10.1007/BF02570481

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  • DOI: https://doi.org/10.1007/BF02570481

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