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arXiv · 2311.17051

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

N. Iorgov·Yu. Zhuravlov
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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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BibTeXRIS

N. Iorgov, Yu. Zhuravlov. 2023-11-28. Long-time asymptotic series for the Painleve II equation: Riemann-Hilbert approach. https://arxiv.org/abs/2311.17051

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