On Threshold Eigenvalues and Resonances for the Linearized NLS Equation

V. Vougalter

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 4, page 448-469
  • ISSN: 0973-5348

Abstract

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We prove the instability of threshold resonances and eigenvalues of the linearized NLS operator. We compute the asymptotic approximations of the eigenvalues appearing from the endpoint singularities in terms of the perturbations applied to the original NLS equation. Our method involves such techniques as the Birman-Schwinger principle and the Feshbach map.

How to cite

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Vougalter, V.. "On Threshold Eigenvalues and Resonances for the Linearized NLS Equation." Mathematical Modelling of Natural Phenomena 5.4 (2010): 448-469. <http://eudml.org/doc/197640>.

@article{Vougalter2010,
abstract = {We prove the instability of threshold resonances and eigenvalues of the linearized NLS operator. We compute the asymptotic approximations of the eigenvalues appearing from the endpoint singularities in terms of the perturbations applied to the original NLS equation. Our method involves such techniques as the Birman-Schwinger principle and the Feshbach map.},
author = {Vougalter, V.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {NLS equation; spectral stability; Birman-Schwinger principle; Feshbach map},
language = {eng},
month = {5},
number = {4},
pages = {448-469},
publisher = {EDP Sciences},
title = {On Threshold Eigenvalues and Resonances for the Linearized NLS Equation},
url = {http://eudml.org/doc/197640},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Vougalter, V.
TI - On Threshold Eigenvalues and Resonances for the Linearized NLS Equation
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/5//
PB - EDP Sciences
VL - 5
IS - 4
SP - 448
EP - 469
AB - We prove the instability of threshold resonances and eigenvalues of the linearized NLS operator. We compute the asymptotic approximations of the eigenvalues appearing from the endpoint singularities in terms of the perturbations applied to the original NLS equation. Our method involves such techniques as the Birman-Schwinger principle and the Feshbach map.
LA - eng
KW - NLS equation; spectral stability; Birman-Schwinger principle; Feshbach map
UR - http://eudml.org/doc/197640
ER -

References

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