Asymptotic stability of small standing solitary waves of the one-dimensional cubic-quintic Schrödinger equation
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929343002836992 |
|---|---|
| author | Martel, Yvan |
| author_facet | Martel, Yvan |
| contents | For the Schrödinger equation with a cubic-quintic, focusing-focusing nonlinearity in one space dimension, this article proves the local asymptotic completeness of the family of small standing solitary waves under even perturbations in the energy space. For this model, perturbative of the integrable cubic Schrödinger equation for small solutions, the linearized equation around a small solitary wave has an internal mode, whose contribution to the dynamics is handled by the Fermi golden rule. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11016 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotic stability of small standing solitary waves of the one-dimensional cubic-quintic Schrödinger equation Martel, Yvan Analysis of PDEs For the Schrödinger equation with a cubic-quintic, focusing-focusing nonlinearity in one space dimension, this article proves the local asymptotic completeness of the family of small standing solitary waves under even perturbations in the energy space. For this model, perturbative of the integrable cubic Schrödinger equation for small solutions, the linearized equation around a small solitary wave has an internal mode, whose contribution to the dynamics is handled by the Fermi golden rule. |
| title | Asymptotic stability of small standing solitary waves of the one-dimensional cubic-quintic Schrödinger equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2312.11016 |