Quasi-linear Stokes phenomenon for the Hastings-McLeod solution of the second Painlevé equation

Details Quasi-linear Stokes phenomenon for the Hastings-McLeod solution of the second Painlevé equation Quasi-linear Stokes phenomenon for the Hastings-McLeod solution of the second Painlevé equation

2004-11-04

arxiv.org/abs/nlin/0411009v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX2e, 22 pages

Scientific paper

Using the Riemann-Hilbert approach, we explicitly construct the asymptotic
$\Psi$-function corresponding to the solution $y\sim\pm\sqrt{-x/2}$ as
$|x|\to\infty$ to the second Painlev\'e equation $y_{xx}=2y^3+xy-\alpha$. We
precisely describe the exponentially small jump in the dominant solution and
the coefficient asymptotics in its power-like expansion.

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