The Riemann-Hilbert-Birkhoff inverse monodromy problem and connection formulae for the third Painlevé transcendents
Abstract
A linear system of ordinary differential equations corresponding by the isomonodromy deformation method to the third Painlevé equation is considered. The surjectivity of the monodromy map generated by this system is proven using the Riemann-Hilbert factorization method. This allows a complete determination of the small x asymptotic behavior of the Painlevé III functions in a sector containing the positive real line. The locations of the singularities within this sector are also given.
Degree
Ph.D.
Advisors
Its, Purdue University.
Subject Area
Applied Mathematics
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