Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potential

The Cauchy problem of nonlinear Schrödinger equation with a harmonic potential for describing the attractive Bose-Einstein condensate under the magnetic trap is considered. We give some sufficient conditions of global existence and finite time blow up of solutions by introducing a family of potentia...

Full description

Bibliographic Details
Main Authors:	Zhang Mingyou, Ahmed Md Salik
Format:	Article
Language:	English
Published:	De Gruyter 2019-08-01
Series:	Advances in Nonlinear Analysis
Subjects:	nonlinear schrödinger equation harmonic potential potential wells global existence invariant sets
Online Access:	https://doi.org/10.1515/anona-2020-0031

id	doaj-8be663389e1641f4ab08ec8ba67b84b4
record_format	Article
spelling	doaj-8be663389e1641f4ab08ec8ba67b84b42021-09-06T19:39:56ZengDe GruyterAdvances in Nonlinear Analysis2191-950X2019-08-019188289410.1515/anona-2020-0031anona-2020-0031Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potentialZhang Mingyou0Ahmed Md Salik1College of Science, Northwest A&F University, Yangling Shaanxi, 712100, People’s Republic of ChinaDepartment of Mathematics and Physics, North South University-1229, Dhaka, BangladeshThe Cauchy problem of nonlinear Schrödinger equation with a harmonic potential for describing the attractive Bose-Einstein condensate under the magnetic trap is considered. We give some sufficient conditions of global existence and finite time blow up of solutions by introducing a family of potential wells. Some different sharp conditions for global existence, and some invariant sets of solutions are also obtained here.https://doi.org/10.1515/anona-2020-0031nonlinear schrödinger equationharmonic potentialpotential wellsglobal existenceinvariant sets
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Zhang Mingyou Ahmed Md Salik
spellingShingle	Zhang Mingyou Ahmed Md Salik Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potential Advances in Nonlinear Analysis nonlinear schrödinger equation harmonic potential potential wells global existence invariant sets
author_facet	Zhang Mingyou Ahmed Md Salik
author_sort	Zhang Mingyou
title	Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potential
title_short	Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potential
title_full	Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potential
title_fullStr	Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potential
title_full_unstemmed	Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potential
title_sort	sharp conditions of global existence for nonlinear schrödinger equation with a harmonic potential
publisher	De Gruyter
series	Advances in Nonlinear Analysis
issn	2191-950X
publishDate	2019-08-01
description	The Cauchy problem of nonlinear Schrödinger equation with a harmonic potential for describing the attractive Bose-Einstein condensate under the magnetic trap is considered. We give some sufficient conditions of global existence and finite time blow up of solutions by introducing a family of potential wells. Some different sharp conditions for global existence, and some invariant sets of solutions are also obtained here.
topic	nonlinear schrödinger equation harmonic potential potential wells global existence invariant sets
url	https://doi.org/10.1515/anona-2020-0031
work_keys_str_mv	AT zhangmingyou sharpconditionsofglobalexistencefornonlinearschrodingerequationwithaharmonicpotential AT ahmedmdsalik sharpconditionsofglobalexistencefornonlinearschrodingerequationwithaharmonicpotential
_version_	1717769697797079040

Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potential

Similar Items