Asymptotics for small data solutions of the Ablowitz-Ladik equation
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909712505634816 |
|---|---|
| author | Stewart, Gavin |
| author_facet | Stewart, Gavin |
| contents | We study the asymptotics for the Ablowitz-Ladik equation. By taking appropriate continuum limits, it can be shown that the behavior of the equation near degenerate frequencies is well approximated by a complex modified Korteweg-de Vries equation. Using this connection, we use the method of space-time resonances to derive a description of the modified scattering behavior of the Ablowitz-Ladik equation, which includes two regions where the solution behaves like a self-similar solution to the complex mKdV equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10496 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotics for small data solutions of the Ablowitz-Ladik equation Stewart, Gavin Analysis of PDEs 34E10 (Primary) 39A12, 33E17 (Secondary) We study the asymptotics for the Ablowitz-Ladik equation. By taking appropriate continuum limits, it can be shown that the behavior of the equation near degenerate frequencies is well approximated by a complex modified Korteweg-de Vries equation. Using this connection, we use the method of space-time resonances to derive a description of the modified scattering behavior of the Ablowitz-Ladik equation, which includes two regions where the solution behaves like a self-similar solution to the complex mKdV equation. |
| title | Asymptotics for small data solutions of the Ablowitz-Ladik equation |
| topic | Analysis of PDEs 34E10 (Primary) 39A12, 33E17 (Secondary) |
| url | https://arxiv.org/abs/2303.10496 |