On the classification of the spectrally stable standing waves of the Hartree problem
Abstract
We consider the fractional Hartree model, with general power non-linearity and space dimension. We construct variationally the "normalized" solutions for the corresponding Choquard-Pekar model - in particular a number of key properties, like smoothness and bell-shapedness are established. As a consequence of the construction, we show that these solitons are spectrally stable as solutions to the time-dependent Hartree model. In addition, we analyze the spectral stability of the Moroz-Van Schaftingen solitons of the classical Hartree problem, in any dimensions and power non-linearity. A full classification is obtained, the main conclusion of which is that only and exactly the "normalized" solutions (which exist only in a portion of the range) are spectrally stable.
Keywords
Cite
@article{arxiv.1702.03374,
title = {On the classification of the spectrally stable standing waves of the Hartree problem},
author = {Vladimir Georgiev and Atanas Stefanov},
journal= {arXiv preprint arXiv:1702.03374},
year = {2018}
}