Existence of Vortices for Nonlinear Schrödinger Equations

In this paper, we study the existence of vortices for two kinds of nonlinear Schr\"{o}dinger equations arising from the Bose-Einstein condensates and geometric optics arguments, respectively. For the Gross-Pitaevskii equation from Bose-Einstein condensates arguments, we introduce the weighted S...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-04
Main Authors: Chen, Shouxin, Su, Guange
Format: Article
Language:English
Subjects:
Bose-Einstein condensates
Boundary conditions
Coercivity
Geometrical optics
Mathematical analysis
Matter & antimatter
Schrodinger equation
Sobolev space
Variational methods
Vortices
Wave propagation
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Chen, Shouxin
Su, Guange
description In this paper, we study the existence of vortices for two kinds of nonlinear Schr\"{o}dinger equations arising from the Bose-Einstein condensates and geometric optics arguments, respectively. For the Gross-Pitaevskii equation from Bose-Einstein condensates arguments, we introduce the weighted Sobolev space on which the corresponding functional is coercive. By using the variational methods, we prove the existence of positive and radially symmetric solutions under different types of boundary condition. And we study another equation arising from geometric optics arguments by constrained minimization method. Furthermore some explicit estimates for the bound of the wave propagation constant are also derived.
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2655333078</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2655333078</sourcerecordid><originalsourceid>FETCH-proquest_journals_26553330783</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mSwcq3ILC5JzUtOVchPUwjLLyrJTE4tVkjLL1Lwy8_LycxLTSxSCE7OKDq8LSUzLz21SMG1sDSxJDM_r5iHgTUtMac4lRdKczMou7mGOHvoFhTlF5amFpfEZ-WXFuUBpeKNzICWGRsbmFsYE6cKACYKN8c</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2655333078</pqid></control><display><type>article</type><title>Existence of Vortices for Nonlinear Schrödinger Equations</title><source>Publicly Available Content Database</source><creator>Chen, Shouxin ; Su, Guange</creator><creatorcontrib>Chen, Shouxin ; Su, Guange</creatorcontrib><description>In this paper, we study the existence of vortices for two kinds of nonlinear Schr\"{o}dinger equations arising from the Bose-Einstein condensates and geometric optics arguments, respectively. For the Gross-Pitaevskii equation from Bose-Einstein condensates arguments, we introduce the weighted Sobolev space on which the corresponding functional is coercive. By using the variational methods, we prove the existence of positive and radially symmetric solutions under different types of boundary condition. And we study another equation arising from geometric optics arguments by constrained minimization method. Furthermore some explicit estimates for the bound of the wave propagation constant are also derived.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Bose-Einstein condensates ; Boundary conditions ; Coercivity ; Geometrical optics ; Mathematical analysis ; Matter &amp; antimatter ; Schrodinger equation ; Sobolev space ; Variational methods ; Vortices ; Wave propagation</subject><ispartof>arXiv.org, 2022-04</ispartof><rights>2022. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2655333078?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>780,784,25752,37011,44589</link.rule.ids></links><search><creatorcontrib>Chen, Shouxin</creatorcontrib><creatorcontrib>Su, Guange</creatorcontrib><title>Existence of Vortices for Nonlinear Schrödinger Equations</title><title>arXiv.org</title><description>In this paper, we study the existence of vortices for two kinds of nonlinear Schr\"{o}dinger equations arising from the Bose-Einstein condensates and geometric optics arguments, respectively. For the Gross-Pitaevskii equation from Bose-Einstein condensates arguments, we introduce the weighted Sobolev space on which the corresponding functional is coercive. By using the variational methods, we prove the existence of positive and radially symmetric solutions under different types of boundary condition. And we study another equation arising from geometric optics arguments by constrained minimization method. Furthermore some explicit estimates for the bound of the wave propagation constant are also derived.</description><subject>Bose-Einstein condensates</subject><subject>Boundary conditions</subject><subject>Coercivity</subject><subject>Geometrical optics</subject><subject>Mathematical analysis</subject><subject>Matter &amp; antimatter</subject><subject>Schrodinger equation</subject><subject>Sobolev space</subject><subject>Variational methods</subject><subject>Vortices</subject><subject>Wave propagation</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mSwcq3ILC5JzUtOVchPUwjLLyrJTE4tVkjLL1Lwy8_LycxLTSxSCE7OKDq8LSUzLz21SMG1sDSxJDM_r5iHgTUtMac4lRdKczMou7mGOHvoFhTlF5amFpfEZ-WXFuUBpeKNzICWGRsbmFsYE6cKACYKN8c</recordid><startdate>20220423</startdate><enddate>20220423</enddate><creator>Chen, Shouxin</creator><creator>Su, Guange</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20220423</creationdate><title>Existence of Vortices for Nonlinear Schrödinger Equations</title><author>Chen, Shouxin ; Su, Guange</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_26553330783</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Bose-Einstein condensates</topic><topic>Boundary conditions</topic><topic>Coercivity</topic><topic>Geometrical optics</topic><topic>Mathematical analysis</topic><topic>Matter &amp; antimatter</topic><topic>Schrodinger equation</topic><topic>Sobolev space</topic><topic>Variational methods</topic><topic>Vortices</topic><topic>Wave propagation</topic><toplevel>online_resources</toplevel><creatorcontrib>Chen, Shouxin</creatorcontrib><creatorcontrib>Su, Guange</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chen, Shouxin</au><au>Su, Guange</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Existence of Vortices for Nonlinear Schrödinger Equations</atitle><jtitle>arXiv.org</jtitle><date>2022-04-23</date><risdate>2022</risdate><eissn>2331-8422</eissn><abstract>In this paper, we study the existence of vortices for two kinds of nonlinear Schr\"{o}dinger equations arising from the Bose-Einstein condensates and geometric optics arguments, respectively. For the Gross-Pitaevskii equation from Bose-Einstein condensates arguments, we introduce the weighted Sobolev space on which the corresponding functional is coercive. By using the variational methods, we prove the existence of positive and radially symmetric solutions under different types of boundary condition. And we study another equation arising from geometric optics arguments by constrained minimization method. Furthermore some explicit estimates for the bound of the wave propagation constant are also derived.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2022-04
issn 2331-8422
language eng
recordid cdi_proquest_journals_2655333078
source Publicly Available Content Database
subjects Bose-Einstein condensates
Boundary conditions
Coercivity
Geometrical optics
Mathematical analysis
Matter & antimatter
Schrodinger equation
Sobolev space
Variational methods
Vortices
Wave propagation
title Existence of Vortices for Nonlinear Schrödinger Equations
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T06%3A57%3A34IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Existence%20of%20Vortices%20for%20Nonlinear%20Schr%C3%B6dinger%20Equations&rft.jtitle=arXiv.org&rft.au=Chen,%20Shouxin&rft.date=2022-04-23&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2655333078%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_26553330783%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2655333078&rft_id=info:pmid/&rfr_iscdi=true