Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 115

The Painleve III Equation and the Iwasawa Decomposition

A. Bobenko, A. Its

Manuscripta math. 87 (1995) 369-377

For the third Painleve 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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