Long-time asymptotic series for the Painleve II equation: Riemann-Hilbert approach

2023/11/28 by Iorgov, N., Zhuravlov, Yu.
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2311.17051

Abstract

We elaborate a systematic way to obtain higher order contributions in the nonlinear steepest descent method for Riemann-Hilbert problem associated with homogeneous Painleve II equation. The problem is reformulated as a matrix factorization problem on two circles and can be solved perturbatively reducing it to finite systems of algebraic linear equations. The method is applied to find explicitly long-time asymptotic behaviour for tau function of Painleve II equation.

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