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Absence of embedded spectrum for nonlinear Schr\"odinger equations linearized around one dimensional ground states

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arxiv 2503.02957 v2 pith:5ZU7GIOY submitted 2025-03-04 math.AP

Charles Collot , Pierre Germain , Eliot Pacherie This is my paper · ORCID
classification math.AP
keywords embeddedgroundlinearizednonlinearodingerschrspectrumstates
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We consider the nonlinear Schr\"odinger equation in dimension one for a generic nonlinearity. We show that ground states do not have embedded eigenvalues in the essential spectrum of their linearized operators.

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  1. Mode stability for self-similar blowup of slightly supercritical NLS: II. high-energy spectrum

    math.AP 2025-07 conditional novelty 7.0 of 10

    For slightly mass-supercritical NLS in 1 to 10 dimensions, no unstable high-energy eigenmodes exist for the linearized self-similar profile operator, which settles its asymptotic stability.

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