Orbital Stability of Optical Solitons in 2d

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Bibliographic Details
Main Author:	Moroni, Sergio
Format:	Preprint
Published:	2024
Subjects:	Analysis of PDEs
Online Access:	Acceder al recurso
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_version_	1866910013548658688
author	Moroni, Sergio
author_facet	Moroni, Sergio
contents	We present a stability result for ground states of a Schrödinger-Poisson system in $(2+1)$ dimension, modelling the propagation of a light beam through a liquid crystal with nonlocal nonlinear response. The core of the proof is a coercivity bound on the second derivative of the action, where non scaling nonlinearities and the coupled system present the major difficulties. In addition we prove existence of a ground state with frequency $σ$ for any $σ\in (0,1)$ as a minimal point over an appropriate Nehari manifold.
format	Preprint
id	arxiv_https___arxiv_org_abs_2404_12890
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Orbital Stability of Optical Solitons in 2d Moroni, Sergio Analysis of PDEs We present a stability result for ground states of a Schrödinger-Poisson system in $(2+1)$ dimension, modelling the propagation of a light beam through a liquid crystal with nonlocal nonlinear response. The core of the proof is a coercivity bound on the second derivative of the action, where non scaling nonlinearities and the coupled system present the major difficulties. In addition we prove existence of a ground state with frequency $σ$ for any $σ\in (0,1)$ as a minimal point over an appropriate Nehari manifold.
title	Orbital Stability of Optical Solitons in 2d
topic	Analysis of PDEs
url	https://arxiv.org/abs/2404.12890

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