Quasi-linear Stokes phenomenon for the Painlevé first equation

Details Quasi-linear Stokes phenomenon for the Painlevé first equation Quasi-linear Stokes phenomenon for the Painlevé first equation

2004-04-14

arxiv.org/abs/nlin/0404026v3

J. Phys. A.: Math. Gen. 37 (2004) 11149-11167

Nonlinear Sciences

Exactly Solvable and Integrable Systems

version accepted for publication

Scientific paper

10.1088/0305-4470/37/46/005

Using the Riemann-Hilbert approach, the $\Psi$-function corresponding to the
solution of the first Painleve equation, $y_{xx}=6y^2+x$, with the asymptotic
behavior $y\sim\pm\sqrt{-x/6}$ as $|x|\to\infty$ is constructed. The
exponentially small jump in the dominant solution and the coefficient
asymptotics in the power-like expansion to the latter are found.

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