Large-time asymptotics for the defocusing Manakov system on nonzero background
Abstract
The Manakov system is a two-component nonlinear Schr\"odinger equation. The long-time asymptotics for the defocusing or focusing Manakov system under nonzero background still remains open. In this paper, we derive the long-time asymptotic formula for the solution of the defocusing Manakov system on nonzero boundary conditions and provide a detailed proof. The solution of the defocusing Manakov system on such nonzero background is first transformed into the solution of a matrix Riemann-Hilbert problem. Then we demonstrate how to conduct the Deift-Zhou steepest descent analysis for this Riemann-Hilbert problem, thereby obtaining the long-time asymptotic behavior of the solution in the space-time soliton region. In this region, the leading order of the solution takes the form of a modulated multisoliton. Apart from the error term, we also discover that the defocusing Manakov system has a dispersive correction term of order , but this term does not exist in the scalar case, and we provide the explicit expression for this dispersion term.
Cite
@article{arxiv.2512.21841,
title = {Large-time asymptotics for the defocusing Manakov system on nonzero background},
author = {Xianguo Geng and Haibing Zhang and Jiao Wei},
journal= {arXiv preprint arXiv:2512.21841},
year = {2025}
}