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The Painlevé III equation and the Iwasawa decomposition. (English) Zbl 0827.35114
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:
35Q53KdV-like (Korteweg-de Vries) equations
53C45Global surface theory (convex surfaces à la A. D. Aleksandrov)
37J35Completely integrable systems, topological structure of phase space, integration methods
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
81R10Infinite-dimensional groups and algebras motivated by physics
References:
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