Stable dipole solitons and soliton complexes in the nonlinear Schrodinger equation with periodically modulated nonlinearity
We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrodinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes b...
Gespeichert in:
Veröffentlicht in: | arXiv.org 2016-06 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | |
---|---|
container_issue | |
container_start_page | |
container_title | arXiv.org |
container_volume | |
creator | Lebedev, M E Alfimov, G L Malomed, Boris A |
description | We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrodinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, the one which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too. |
doi_str_mv | 10.48550/arxiv.1604.02592 |
format | Article |
fullrecord | <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_1604_02592</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2080010296</sourcerecordid><originalsourceid>FETCH-LOGICAL-a526-f5e13a2f01c43944fcbe0d75ce5a58a9f1b45384122ab8e3231831d10d8a27a3</originalsourceid><addsrcrecordid>eNpFkE1LAzEQhoMgWKo_wJMBz1vzuc0epfgFBQ_1vsxusjYlTbZJVlv8866t4ullmOcdhgeha0pmQklJ7iDu7ceMlkTMCJMVO0MTxjktlGDsAl2ltCGEsHLOpOQT9LXK0DiDte3DGCk4m4NPGLz-G3Abtr0ze5Ow9TivDfbBO-sNRLxq1zFo699NxGY3QLYj_2nzGvcm2nHTgnMHvA16cJCN_q_afLhE5x24ZK5-c4pWjw9vi-di-fr0srhfFiBZWXTSUA6sI7QVvBKiaxtD9Fy2RoJUUHW0EZIrQRmDRhnOOFWcakq0AjYHPkU3p6tHMXUf7Rbiof4RVB8FjcTtiehj2A0m5XoThujHl2pGFCGUsKrk3719a8M</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2080010296</pqid></control><display><type>article</type><title>Stable dipole solitons and soliton complexes in the nonlinear Schrodinger equation with periodically modulated nonlinearity</title><source>arXiv.org</source><source>Free E- Journals</source><creator>Lebedev, M E ; Alfimov, G L ; Malomed, Boris A</creator><creatorcontrib>Lebedev, M E ; Alfimov, G L ; Malomed, Boris A</creatorcontrib><description>We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrodinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, the one which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1604.02592</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Bose-Einstein condensates ; Cubic lattice ; Dipoles ; Lattices (mathematics) ; Mathematical analysis ; Mathematical models ; Mathematics - Mathematical Physics ; Nonlinear equations ; Nonlinear optics ; Nonlinearity ; Physics - Mathematical Physics ; Physics - Pattern Formation and Solitons ; Physics - Quantum Gases ; Schrodinger equation ; Solitary waves</subject><ispartof>arXiv.org, 2016-06</ispartof><rights>2016. 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><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,784,885,27925</link.rule.ids><backlink>$$Uhttps://doi.org/10.1063/1.4958710$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.48550/arXiv.1604.02592$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Lebedev, M E</creatorcontrib><creatorcontrib>Alfimov, G L</creatorcontrib><creatorcontrib>Malomed, Boris A</creatorcontrib><title>Stable dipole solitons and soliton complexes in the nonlinear Schrodinger equation with periodically modulated nonlinearity</title><title>arXiv.org</title><description>We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrodinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, the one which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.</description><subject>Bose-Einstein condensates</subject><subject>Cubic lattice</subject><subject>Dipoles</subject><subject>Lattices (mathematics)</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematics - Mathematical Physics</subject><subject>Nonlinear equations</subject><subject>Nonlinear optics</subject><subject>Nonlinearity</subject><subject>Physics - Mathematical Physics</subject><subject>Physics - Pattern Formation and Solitons</subject><subject>Physics - Quantum Gases</subject><subject>Schrodinger equation</subject><subject>Solitary waves</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNpFkE1LAzEQhoMgWKo_wJMBz1vzuc0epfgFBQ_1vsxusjYlTbZJVlv8866t4ullmOcdhgeha0pmQklJ7iDu7ceMlkTMCJMVO0MTxjktlGDsAl2ltCGEsHLOpOQT9LXK0DiDte3DGCk4m4NPGLz-G3Abtr0ze5Ow9TivDfbBO-sNRLxq1zFo699NxGY3QLYj_2nzGvcm2nHTgnMHvA16cJCN_q_afLhE5x24ZK5-c4pWjw9vi-di-fr0srhfFiBZWXTSUA6sI7QVvBKiaxtD9Fy2RoJUUHW0EZIrQRmDRhnOOFWcakq0AjYHPkU3p6tHMXUf7Rbiof4RVB8FjcTtiehj2A0m5XoThujHl2pGFCGUsKrk3719a8M</recordid><startdate>20160630</startdate><enddate>20160630</enddate><creator>Lebedev, M E</creator><creator>Alfimov, G L</creator><creator>Malomed, Boris A</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><scope>AKZ</scope><scope>ALA</scope><scope>GOX</scope></search><sort><creationdate>20160630</creationdate><title>Stable dipole solitons and soliton complexes in the nonlinear Schrodinger equation with periodically modulated nonlinearity</title><author>Lebedev, M E ; Alfimov, G L ; Malomed, Boris A</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a526-f5e13a2f01c43944fcbe0d75ce5a58a9f1b45384122ab8e3231831d10d8a27a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Bose-Einstein condensates</topic><topic>Cubic lattice</topic><topic>Dipoles</topic><topic>Lattices (mathematics)</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Mathematics - Mathematical Physics</topic><topic>Nonlinear equations</topic><topic>Nonlinear optics</topic><topic>Nonlinearity</topic><topic>Physics - Mathematical Physics</topic><topic>Physics - Pattern Formation and Solitons</topic><topic>Physics - Quantum Gases</topic><topic>Schrodinger equation</topic><topic>Solitary waves</topic><toplevel>online_resources</toplevel><creatorcontrib>Lebedev, M E</creatorcontrib><creatorcontrib>Alfimov, G L</creatorcontrib><creatorcontrib>Malomed, Boris A</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Access via ProQuest (Open Access)</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><collection>arXiv Mathematics</collection><collection>arXiv Nonlinear Science</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lebedev, M E</au><au>Alfimov, G L</au><au>Malomed, Boris A</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stable dipole solitons and soliton complexes in the nonlinear Schrodinger equation with periodically modulated nonlinearity</atitle><jtitle>arXiv.org</jtitle><date>2016-06-30</date><risdate>2016</risdate><eissn>2331-8422</eissn><abstract>We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrodinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, the one which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1604.02592</doi><oa>free_for_read</oa></addata></record> |
fulltext | fulltext |
identifier | EISSN: 2331-8422 |
ispartof | arXiv.org, 2016-06 |
issn | 2331-8422 |
language | eng |
recordid | cdi_arxiv_primary_1604_02592 |
source | arXiv.org; Free E- Journals |
subjects | Bose-Einstein condensates Cubic lattice Dipoles Lattices (mathematics) Mathematical analysis Mathematical models Mathematics - Mathematical Physics Nonlinear equations Nonlinear optics Nonlinearity Physics - Mathematical Physics Physics - Pattern Formation and Solitons Physics - Quantum Gases Schrodinger equation Solitary waves |
title | Stable dipole solitons and soliton complexes in the nonlinear Schrodinger equation with periodically modulated nonlinearity |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-23T13%3A08%3A57IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Stable%20dipole%20solitons%20and%20soliton%20complexes%20in%20the%20nonlinear%20Schrodinger%20equation%20with%20periodically%20modulated%20nonlinearity&rft.jtitle=arXiv.org&rft.au=Lebedev,%20M%20E&rft.date=2016-06-30&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1604.02592&rft_dat=%3Cproquest_arxiv%3E2080010296%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2080010296&rft_id=info:pmid/&rfr_iscdi=true |