The cubic-quintic nonlinear Schr\"odinger equation with inverse-square potential
Analysis of PDEs
2024-12-16 v1
Abstract
We consider the nonlinear Schr\"odinger equation in three space dimensions with a focusing cubic nonlinearity and defocusing quintic nonlinearity and in the presence of an external inverse-square potential. We establish scattering in the region of the mass-energy plane where the virial functional is guaranteed to be positive. Our result parallels the scattering result of \cite{R.Killip, T. Oh, O. Pocovnicu, and M. Visan} in the setting of the standard cubic-quintic NLS.
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Cite
@article{arxiv.2112.07079,
title = {The cubic-quintic nonlinear Schr\"odinger equation with inverse-square potential},
author = {Alex H. Ardila and Jason Murphy},
journal= {arXiv preprint arXiv:2112.07079},
year = {2024}
}
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32 pages