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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2003-2004 MATHEMATICS COLLOQUIUM SERIES 10/14/03 Colloquium DR. ALEXANDER ITS INDIANA UNIVERSITY PURDUE UNIVERSITY INDIANAPOLIS Quasi-linear Stokes Phenomenon for the Second Painlevé Transcendent Abstract:  Using the Riemann-Hilbert approach, we study the quasi-linear Stokes phenomenon for the second Painlevé equation . The precise description of the exponentially small jump in the dominant solution approaching  as  tends to infinity is given. The asymptotics of the coefficients of the formal power series, which asymptotically represents the dominant solution, is found. This is joint work with Andrei Kapaev.