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Generic non-selfadjoint Zakharov-Shabat operators


Kappeler, T; Lohrmann, Philipp; Topalov, Peter J (2014). Generic non-selfadjoint Zakharov-Shabat operators. Mathematische Annalen, 359(1-2):427-470.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:9 January 2014
Deposited On:07 Oct 2014 08:54
Last Modified:05 Apr 2016 18:24
Publisher:Springer
ISSN:0025-5831
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/s00208-013-1004-4

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