On the asymptotic stability of ground states of the pure power NLS on the line at 3rd and 4th order Fermi Golden Rule
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910907161903104 |
|---|---|
| author | Cuccagna, Scipio Maeda, Masaya |
| author_facet | Cuccagna, Scipio Maeda, Masaya |
| contents | Assuming as hypotheses the results proved numerically by Chang et al. \cite{Chang} for the exponent $p\in (3,5)$, we prove that some of the ground states of the nonlinear Schrödinger equation (NLS) with pure power nonlinearity of exponent $p$ in the line are asymptotically stable for a certain set of values of the exponent $p$ where the FGR occurs by means of a discrete mode 3rd or 4th order power interaction with the continuous mode. For the 3rd the result is true for generic $p$ while for the 4th order case we assume that there are $p$'s satisfying Fermi Golden rule and the non-resonance condition of the threshold of the continuous spectrum of the linearization. The argument is similar to our recent result valid for $p$ near 3 contained in \cite{CM24D1}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the asymptotic stability of ground states of the pure power NLS on the line at 3rd and 4th order Fermi Golden Rule Cuccagna, Scipio Maeda, Masaya Analysis of PDEs 35Q55 Assuming as hypotheses the results proved numerically by Chang et al. \cite{Chang} for the exponent $p\in (3,5)$, we prove that some of the ground states of the nonlinear Schrödinger equation (NLS) with pure power nonlinearity of exponent $p$ in the line are asymptotically stable for a certain set of values of the exponent $p$ where the FGR occurs by means of a discrete mode 3rd or 4th order power interaction with the continuous mode. For the 3rd the result is true for generic $p$ while for the 4th order case we assume that there are $p$'s satisfying Fermi Golden rule and the non-resonance condition of the threshold of the continuous spectrum of the linearization. The argument is similar to our recent result valid for $p$ near 3 contained in \cite{CM24D1}. |
| title | On the asymptotic stability of ground states of the pure power NLS on the line at 3rd and 4th order Fermi Golden Rule |
| topic | Analysis of PDEs 35Q55 |
| url | https://arxiv.org/abs/2405.11763 |