XIV Conference of Young Scientists "Problems of Theoretical Physics"

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

16 Jan 2024, 16:25

20m

BITP & Zoom

Oral talk Mathematical Physics Afternoon session 1

Speaker

Yurii Zhuravlov (Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine)

Description

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.