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Kappeler, T; Lohrmann, Philipp; Topalov, Peter J (2014). Generic non-selfadjoint Zakharov-Shabat operators. Mathematische Annalen, 359(1-2):427-470.
In this paper we develop tools to study within a family of non-selfadjoint operators L(φ) depending on a parameter φ in a real Hilbert space, those with (partially) simple spectrum. As a case study we consider the Zakharov-Shabat operators L(φ) appearing in the Lax pair of the focusing NLS on the circle. In particular, the main result implies that the set of potentials φ of Sobolev class HN, N≥ 0, so that all non real eigenvalues of L(φ) are simple, is path connected and dense.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics |
| Language: | English |
| Date: | 9 January 2014 |
| Deposited On: | 07 Oct 2014 08:54 |
| Last Modified: | 12 Aug 2024 01:44 |
| Publisher: | Springer |
| ISSN: | 0025-5831 |
| OA Status: | Closed |
| Free access at: | Publisher DOI. An embargo period may apply. |
| Publisher DOI: | https://doi.org/10.1007/s00208-013-1004-4 |
Kappeler, T