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Quasi-linear Stokes phenomenon for the second Painlev\'e transcendent

Presented by: 
A Kapaev [Steklov]
Monday 5th November 2001 - 15:00 to 16:00
INI Seminar Room 1
Using the Riemann-Hilbert approach, we study the quasi-linear Stokes phenomenon for the second Painlev\'e equation $y_{xx}=2y^3+xy-\alpha$. The precise description of the exponentially small jump in the dominant solution approaching $\alpha/x$ as $|x|\to\infty$ is given. For the asymptotic power expansion of the dominant solution, the asymptotics of the coefficients is found.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons