Painlev\'e-type asymptotics for the defocusing Manakov system with nonzero boundary conditions
Exactly Solvable and Integrable Systems
2026-03-20 v1
Abstract
We investigate the long-time asymptotic behavior of a class of solutions to the defocusing Manakov system under nonzero boundary conditions. These solutions are characterized by a matrix Riemann Hilbert problem. We find that they exhibit interesting asymptotic behavior within a narrow transition zone in the - plane. We determine the leading-order asymptotic term and the error bound in this region, and we demonstrate that the leading term can be expressed in terms of the Hastings-McLeod solution of the Painlev\'e II equation. The proof is rigorously established by applying the Deift-Zhou nonlinear steepest descent method to the associated Riemann Hilbert problem.
Cite
@article{arxiv.2603.18430,
title = {Painlev\'e-type asymptotics for the defocusing Manakov system with nonzero boundary conditions},
author = {Haibing Zhang and Xianguo Geng and Ruomeng Li and Huan Liu},
journal= {arXiv preprint arXiv:2603.18430},
year = {2026}
}