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Zbl 0827.35114
Bobenko, Alexander; Its, Alexander
The Painlevé III equation and the Iwasawa decomposition. (English)
[J] Manuscr. Math. 87, No.3, 369-377 (1995). ISSN 0025-2611; ISSN 1432-1785/e

Summary: 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.

MSC 2000:: *35Q53 KdV-like equations
53C45 Global surface theory (a la A.D. Aleksandrov)
37J35 Completely integrable systems, etc.
37K10 Completely integrable systems etc.
81R10 Repres. of infinite-dim. groups and algebras from quantum theory

Keywords: monodromy data; data of the approach of Dorfmeister-Pedit-Wu; Iwasawa decomposition of the loop groups; Cauchy data at zero

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