Details

Autor(en) / Beteiligte

• Buchstaber, Victor M
• Konstantinou-Rizos, Sotiris
• Mikhailov, Alexander V

Titel

Movable Poles of Painlevé I Transcendents and Singularities of Monodromy Data Manifolds

Ist Teil von

• Recent Developments in Integrable Systems and Related Topics of Mathematical Physics, 2018, Vol.273, p.24-37

Ort / Verlag

Switzerland: Springer International Publishing AG

Erscheinungsjahr

2018

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We consider a classification of solutions to the first Painlevé  equation with respect to distribution of their poles at infinity. A connection is found between singularities of two-dimensional monodromy data manifold and analytic properties of solutions parametrized by this manifold. It is proved that solutions of Painlevé  I equation have no poles at infinity at a given critical sector of the complex plane iff the related monodromy data belong to the singular submanifold. Such solutions coincide with the class of “truncated” solutions (intégrales tronquée) by classification of P. Boutroux. We derive further classification based on decomposition of singularities of monodromy data manifold.