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

2004/11/04 by A. A. Kapaev, Andrei Kapaev, Kapaev, A. A.
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons #Random Matrices and Applications #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0411009

LaTeX2e, 22 pages

openalex publication_date 2004/11/04 · arxiv created 2004/11/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the Riemann-Hilbert approach, we explicitly construct the asymptotic Ψ-function corresponding to the solution y∼±√(-x/2) as |x|→∞ to the second Painlevé equation y_xx=2y³+xy-α. We precisely describe the exponentially small jump in the dominant solution and the coefficient asymptotics in its power-like expansion.

Citations

• Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II

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