On the spectrum of the periodic focusing Zakharov-Shabat operator
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2020
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916474306691072 |
|---|---|
| author | Biondini, Gino Oregero, Jeffrey Tovbis, Alexander |
| author_facet | Biondini, Gino Oregero, Jeffrey Tovbis, Alexander |
| contents | The spectrum of the focusing Zakharov-Shabat operator on the circle is studied, and its explicit dependence on the presence of a semiclassical parameter is also considered. Several new results are obtained. In particular: (i) it is proved that the resolvent set is comprised of two connected components, (ii) new bounds on the location of the Floquet and Dirichlet spectra are obtained, some of which depend explicitly on the value of the semiclassical parameter, (iii) it is proved that the spectrum localizes to a "cross" in the spectral plane in the semiclassical limit. The results are illustrated by discussing several examples in which the spectrum is computed analytically or numerically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_04263 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the spectrum of the periodic focusing Zakharov-Shabat operator Biondini, Gino Oregero, Jeffrey Tovbis, Alexander Spectral Theory Mathematical Physics Exactly Solvable and Integrable Systems The spectrum of the focusing Zakharov-Shabat operator on the circle is studied, and its explicit dependence on the presence of a semiclassical parameter is also considered. Several new results are obtained. In particular: (i) it is proved that the resolvent set is comprised of two connected components, (ii) new bounds on the location of the Floquet and Dirichlet spectra are obtained, some of which depend explicitly on the value of the semiclassical parameter, (iii) it is proved that the spectrum localizes to a "cross" in the spectral plane in the semiclassical limit. The results are illustrated by discussing several examples in which the spectrum is computed analytically or numerically. |
| title | On the spectrum of the periodic focusing Zakharov-Shabat operator |
| topic | Spectral Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2010.04263 |