Generic non-selfadjoint Zakharov-Shabat operators

T. Kappeler; P. Lohrmann; P. Topalov

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arXiv · 1204.5200

Generic non-selfadjoint Zakharov-Shabat operators

T. Kappeler·P. Lohrmann·P. Topalov

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Abstract

In this paper we develop tools to study families of non-selfadjoint operators $L(φ), φ\in P$, characterized by the property that the spectrum of $L(φ)$ is (partially) simple. As a case study we consider the Zakharov-Shabat operators $L(φ)$ appearing in the Lax pair of the focusing NLS on the circle. The main result says that the set of potentials $φ$ of Sobolev class $H^N, N \geq 0$, so that all small eigenvalues of $L(φ)$ are simple, is path connected and dense.

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BibTeX RIS

T. Kappeler, P. Lohrmann, P. Topalov. 2012-12-18. Generic non-selfadjoint Zakharov-Shabat operators. https://arxiv.org/abs/1204.5200

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