On the gap property of a linearized NLS operator

We consider general non-radial linearization about the ground state to the cubic nonlinear Schr\"odinger equation in dimension three. We introduce a new {compare-and-conquer} approach and rigorously prove that the interval \((0, 1]\) does not contain any eigenvalue of \(L_+\) or \(L_-\). The me...

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Bibliographic Details
Published inarXiv.org
Main Authors Li, Dong, Yang, Kai
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 27.10.2021
Subjects
Eigenvalues
Linearization
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Summary:We consider general non-radial linearization about the ground state to the cubic nonlinear Schr\"odinger equation in dimension three. We introduce a new {compare-and-conquer} approach and rigorously prove that the interval \((0, 1]\) does not contain any eigenvalue of \(L_+\) or \(L_-\). The method can be adapted to many other spectral problems.
ISSN:2331-8422