We study the spectrum of the linearized NLS equation in three dimensions in association with the energy spectrum. We prove that unstable eigenvalues of the linearized NLS problem are related to negative eigenvalues of the energy spectrum, while neutrally stable eigenvalues may have both positive and negative energies. The nonsingular part of the neutrally stable essential spectrum is always related to the positive energy spectrum. We derive bounds on the number of unstable eigenvalues of the linearized NLS problem and study bifurcations of embedded eigenvalues of positive and negative energies. We develop the L2-scattering theory for the linearized NLS operators and recover results of Grillakis with a Fermi golden rule

Spectra of positive and negative energies in the linearization of the NLS problem / Cuccagna, Scipio; Dmitry, Pelinovsky; Vitali, Vougalter. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - STAMPA. - 58:1(2005), pp. 1-29. [10.1002/cpa.20050]

Spectra of positive and negative energies in the linearization of the NLS problem

CUCCAGNA, Scipio;
2005

Abstract

We study the spectrum of the linearized NLS equation in three dimensions in association with the energy spectrum. We prove that unstable eigenvalues of the linearized NLS problem are related to negative eigenvalues of the energy spectrum, while neutrally stable eigenvalues may have both positive and negative energies. The nonsingular part of the neutrally stable essential spectrum is always related to the positive energy spectrum. We derive bounds on the number of unstable eigenvalues of the linearized NLS problem and study bifurcations of embedded eigenvalues of positive and negative energies. We develop the L2-scattering theory for the linearized NLS operators and recover results of Grillakis with a Fermi golden rule
2005
58
1
1
29
Spectra of positive and negative energies in the linearization of the NLS problem / Cuccagna, Scipio; Dmitry, Pelinovsky; Vitali, Vougalter. - In: COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS. - ISSN 0010-3640. - STAMPA. - 58:1(2005), pp. 1-29. [10.1002/cpa.20050]
Cuccagna, Scipio; Dmitry, Pelinovsky; Vitali, Vougalter
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/421146
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