Quasi-linear Stokes phenomenon for the second Painlev transcendent

2001/08/07 by A. R. Its, A. A. Kapaev, Andrei Kapaev · 2 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Exponential growth #Jump #Mathematical analysis #Mathematical physics #Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Ocean Waves and Remote Sensing #Phenomenon #Physics #Quantum mechanics #Riemann hypothesis #nlin.SI

paper · pdf · doi:10.1088/0951-7715/16/1/321

published as Nonlinearity 16 (2003) 363-386 · 19 pages, LaTeX

arxiv created 2001/08/07 · openalex publication_date 2002/12/18 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Using the Riemann–Hilbert approach, we study the quasi-linear Stokes phenomenon for the second Painlevé equation y xx = 2 y 3 + xy −α. The precise description of the exponentially small jump in the dominant solution approaching α/ x as | x |→ ∞ is given. For the asymptotic power expansion of the dominant solution, the coefficient asymptotics is computed.

Citations

• On Borel summation and Stokes phenomena for rank-1 nonlinear systems of ordinary differential equations
• Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II

Cited by

• Fredholm Determinants and Pole-free Solutions to the Noncommutative Painlevé II Equation
• Tronquée Solutions of the Third and Fourth Painlevé Equations