Painlevé-type asymptotics for the defocusing Manakov system with nonzero boundary conditions
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917352667348992 |
|---|---|
| author | Zhang, Haibing Geng, Xianguo Li, Ruomeng Liu, Huan |
| author_facet | Zhang, Haibing Geng, Xianguo Li, Ruomeng Liu, Huan |
| contents | 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 $3 \times 3$ matrix Riemann Hilbert problem. We find that they exhibit interesting asymptotic behavior within a narrow transition zone in the $x$-$t$ 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 Painlevé II equation. The proof is rigorously established by applying the Deift-Zhou nonlinear steepest descent method to the associated Riemann Hilbert problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18430 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Painlevé-type asymptotics for the defocusing Manakov system with nonzero boundary conditions Zhang, Haibing Geng, Xianguo Li, Ruomeng Liu, Huan Exactly Solvable and Integrable Systems 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 $3 \times 3$ matrix Riemann Hilbert problem. We find that they exhibit interesting asymptotic behavior within a narrow transition zone in the $x$-$t$ 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 Painlevé II equation. The proof is rigorously established by applying the Deift-Zhou nonlinear steepest descent method to the associated Riemann Hilbert problem. |
| title | Painlevé-type asymptotics for the defocusing Manakov system with nonzero boundary conditions |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2603.18430 |