Abstract
We consider a classification of solutions to the first Painleve 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 Painleve 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 (integrales tronquee) by classification of P. Boutroux. We derive further classification based on decomposition of singularities of monodromy data manifold.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
