Analytical solutions for the spin-1 Bose-Einstein condensate in a harmonic trap
The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear Schrödinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensiona...
Saved in:
| Published in | Frontiers of physics Vol. 8; no. 3; pp. 319 - 327 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Higher Education Press
01.06.2013
SP Higher Education Press Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2095-0462 2095-0470 |
| DOI | 10.1007/s11467-013-0332-x |
Cover
| Abstract | The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear Schrödinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case. |
|---|---|
| AbstractList | The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear Schrödinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case. The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear SchrSdinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case. |
| Author | 石玉仁 王雪玲 王光辉 刘丛波 周志刚 杨红娟 |
| AuthorAffiliation | College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China |
| Author_xml | – sequence: 1 fullname: 石玉仁 王雪玲 王光辉 刘丛波 周志刚 杨红娟 |
| BookMark | eNp9kctqHDEQRUVwII4zH5CdgteKVVI_l7ZxHjDgjbMWak31tExbaqs0YP99NLRxIItZlQrq1K179ZmdhRiQsa8gv4OU7RUBVE0rJGghtVbi5QM7V7Kvhaxaefb-btQntiF6lFICtFXpz9n9dbDza_bOzpzifMg-BuJjTDxPyGnxQQC_iYTizgfK6AN3MewwkM3IS2f5ZNNTDN7xnOzyhX0c7Uy4easX7M-Pu4fbX2J7__P37fVWON1DFjj0HYy60q5Dp7sRtKprdMPgallZRLCdAqWGatBdXTd9Yys3ds7JUfdtDUpfsMt175Li8wEpm8d4SMULGdVD16hGN1CmYJ1yKRIlHM2S_JNNrwakOUZn1uhMic4cozMvhWn_Y5zP9phL8efnk6RaSSoqYY_p302noG6FJr-fMOFuSUhkxlT0PKbT6Le3S6cY9s9F8t1e-dtKt6rWfwHl0KHv |
| CitedBy_id | crossref_primary_10_1007_s11467_021_1134_1 |
| Cites_doi | 10.1103/PhysRevA.82.023612 10.1143/JPSJ.67.1822 10.1016/j.cnsns.2008.04.013 10.1016/j.cnsns.2009.09.002 10.1103/PhysRevA.72.023610 10.1103/PhysRevA.60.4857 10.1103/PhysRevA.77.033612 10.1103/PhysRevA.69.033606 10.1103/PhysRevLett.88.093201 10.1137/070698488 10.1108/09615531211188766 10.1016/j.cnsns.2012.01.030 10.1007/978-3-642-25132-0 10.1016/j.ijmecsci.2010.09.007 10.1007/s11467-011-0213-0 10.1103/PhysRevA.81.025604 10.1016/j.amc.2012.02.004 10.1016/j.cpc.2007.04.007 10.1201/9780203491164 10.1016/j.aml.2010.06.003 10.7498/aps.59.67 10.1134/S1054660X06040220 10.1103/PhysRevA.84.053607 10.1103/PhysRevLett.92.140403 10.1103/PhysRevA.83.013626 10.1103/PhysRevLett.80.2027 10.1103/PhysRevLett.101.040402 10.1103/PhysRevA.64.053602 10.1038/24567 10.1515/ijnsns.2011.020 10.1103/PhysRevLett.90.230401 10.1016/S0020-7462(02)00174-9 10.1103/PhysRevLett.81.742 10.1103/PhysRevA.75.023617 10.1016/j.compfluid.2009.12.007 10.1007/s11467-011-0219-7 10.1103/PhysRevLett.97.180412 10.4310/MAA.2010.v17.n1.a2 10.1016/j.cnsns.2009.09.019 10.1103/PhysRevE.67.046706 10.1016/j.ijthermalsci.2010.12.014 10.7498/aps.55.1555 |
| ContentType | Journal Article |
| Copyright | Copyright reserved, 2014, Higher Education Press and Springer-Verlag Berlin Heidelberg Higher Education Press and Springer-Verlag Berlin Heidelberg 2013 Higher Education Press and Springer-Verlag Berlin Heidelberg 2013. |
| Copyright_xml | – notice: Copyright reserved, 2014, Higher Education Press and Springer-Verlag Berlin Heidelberg – notice: Higher Education Press and Springer-Verlag Berlin Heidelberg 2013 – notice: Higher Education Press and Springer-Verlag Berlin Heidelberg 2013. |
| DBID | 2RA 92L CQIGP ~WA AAYXX CITATION 3V. 7XB 88I 8FE 8FG 8FK ABUWG AEUYN AFKRA ARAPS AZQEC BENPR BGLVJ BHPHI BKSAR CCPQU DWQXO GNUQQ HCIFZ M2P P5Z P62 PCBAR PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI Q9U |
| DOI | 10.1007/s11467-013-0332-x |
| DatabaseName | 维普_期刊 中文科技期刊数据库-CALIS站点 中文科技期刊数据库-7.0平台 中文科技期刊数据库- 镜像站点 CrossRef ProQuest Central (Corporate) ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ProQuest Central (Alumni) ProQuest One Sustainability (subscription) ProQuest Central UK/Ireland Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Central Technology Collection Natural Science Collection Earth, Atmospheric & Aquatic Science Collection ProQuest One Community College ProQuest Central Korea ProQuest Central Student SciTech Premium Collection Science Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Earth, Atmospheric & Aquatic Science Database ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central Basic |
| DatabaseTitle | CrossRef ProQuest Central Student Technology Collection ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central Earth, Atmospheric & Aquatic Science Collection ProQuest One Applied & Life Sciences ProQuest One Sustainability Natural Science Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies & Aerospace Collection ProQuest Science Journals (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest One Academic Eastern Edition Earth, Atmospheric & Aquatic Science Database ProQuest Technology Collection ProQuest SciTech Collection Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition ProQuest One Academic ProQuest Central (Alumni) ProQuest One Academic (New) |
| DatabaseTitleList | ProQuest Central Student |
| Database_xml | – sequence: 1 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| DocumentTitleAlternate | Analytical solutions for the spin-1 Bose-Einstein condensate in a harmonic trap |
| EISSN | 2095-0470 |
| EndPage | 327 |
| ExternalDocumentID | 10_1007_s11467_013_0332_x 10.1007/s11467-013-0332-x 46243725 |
| GroupedDBID | -5F -5G -BR -EM -~C .VR 06D 0R~ 0VY 1-T 29~ 2J2 2JN 2JY 2KG 2KM 2LR 2RA 2~H 30V 4.4 406 408 40E 5VS 88I 92L 95- 95. 95~ 96X AAAVM AABHQ AACDK AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABDZT ABECU ABFTV ABHQN ABJNI ABJOX ABKCH ABKTR ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACSNA ACZOJ ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEUYN AEVLU AEXYK AFBBN AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AOCGG ARAPS ARMRJ ASPBG AVWKF AXYYD AZFZN AZQEC B-. BDATZ BENPR BGLVJ BGNMA BHPHI BKSAR BSONS CCPQU CQIGP CSCUP DDRTE DNIVK DPUIP DWQXO EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 H13 HCIFZ HF~ HG6 HMJXF HRMNR HVGLF HZ~ IAO IEA IJ- IKXTQ IWAJR IXD I~Z J-C JBSCW JZLTJ KOV LLZTM M2P M4Y MA- N2Q NPVJJ NQJWS NU0 O9- O9J P4S P9T PCBAR PF0 PT4 R89 R9I ROL RSV S16 S3B SAP SCL SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPH SPISZ SRMVM SSLCW STPWE SZN TSG TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z88 ZMTXR ~A9 ~WA AAFGU AAYFA ABFGW ABKAS ACBMV ACBRV ACIPQ ACTTH ACVWB ACWMK ADMDM ADOXG AEFTE AESTI AEVTX AFNRJ AGGBP AIMYW AJDOV UNUBA ACPIV -SA -S~ AAPKM AAXDM AAYXX ABFSG ACSTC ADHKG AEZWR AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CAJEA CITATION PHGZM PHGZT Q-- TGP U1G U5K 3V. 7XB 8FE 8FG 8FK P62 PKEHL PQEST PQGLB PQQKQ PQUKI PUEGO Q9U |
| ID | FETCH-LOGICAL-c391t-eb981f343c8ec38f13255ecbbc504aee1a82122b4b3855696a4cf8cc0f3975123 |
| IEDL.DBID | 8FG |
| ISSN | 2095-0462 |
| IngestDate | Sat Aug 23 13:16:18 EDT 2025 Thu Apr 24 23:13:02 EDT 2025 Tue Jul 01 03:04:51 EDT 2025 Fri Feb 21 02:38:02 EST 2025 Tue Feb 27 04:42:59 EST 2024 Tue Dec 31 07:00:26 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | analytical solution homotopy analysis method Gross-Pitaevskii equation spin-1 Bose-Einstein condensate |
| Language | English |
| License | This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. http://www.springer.com/tdm |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c391t-eb981f343c8ec38f13255ecbbc504aee1a82122b4b3855696a4cf8cc0f3975123 |
| Notes | spin-1 Bose-Einstein condensate, Gross-Pitaevskii equation, homotopy analysis method, analytical solution Yu-Ren Shi ,Xue-Ling Wang , Guang-Hui Wang, Cong-Bo Liu , Zhi-Gang Zhou, Hong-Juan Yang （College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China） 11-5994/O4 The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear SchrSdinger equation used in simulation of spin-1 Bose-Einstein condensates trapped in a harmonic potential. We investigate the one-dimensional case and get the approximate analytical solutions successfully. Comparisons between the analytical solutions and the numerical solutions have been made. The results indicate that they are in agreement well with each other when the atomic interaction is weakly. We also find a class of exact solutions for the stationary states of the spin-1 system with harmonic potential for a special case. analytical solution Document accepted on :2013-03-24 homotopy analysis method Document received on :2012-12-05 Gross-Pitaevskii equation spin-1 Bose-Einstein condensate ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://journal.hep.com.cn/fop/EN/10.1007/s11467-013-0332-x |
| PQID | 2918626361 |
| PQPubID | 2044425 |
| PageCount | 9 |
| ParticipantIDs | proquest_journals_2918626361 crossref_primary_10_1007_s11467_013_0332_x crossref_citationtrail_10_1007_s11467_013_0332_x springer_journals_10_1007_s11467_013_0332_x higheredpress_frontiers_10_1007_s11467_013_0332_x chongqing_primary_46243725 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2013-06-01 |
| PublicationDateYYYYMMDD | 2013-06-01 |
| PublicationDate_xml | – month: 06 year: 2013 text: 2013-06-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Heidelberg |
| PublicationPlace_xml | – name: Heidelberg |
| PublicationSubtitle | Selected Publications from Chinese Universities |
| PublicationTitle | Frontiers of physics |
| PublicationTitleAbbrev | Front. Phys |
| PublicationTitleAlternate | Frontiers of Physics in China |
| PublicationYear | 2013 |
| Publisher | Higher Education Press SP Higher Education Press Springer Nature B.V |
| Publisher_xml | – name: Higher Education Press – name: SP Higher Education Press – name: Springer Nature B.V |
| References | BarnettRTurnerADemlerEPhys. Rev. Lett.200697181804122006PhRvL..97r0412B10.1103/PhysRevLett.97.180412 ChengYLiaoS JCommun. Nonlinear Sci. Numer. Simul.20064775 GuanX WFront. Phys.201271810.1007/s11467-011-0213-0 KlausenN NBohnJ LGreeneC HPhys. Rev. A20016450536022001PhRvA..64e3602K10.1103/PhysRevA.64.053602 TurkyilmazogluMCommun. Nonlinear Sci. Numer. Simul.20121711409729303092012CNSNS..17.4097T0608193410.1016/j.cnsns.2012.01.030 OhmiTMachidaKJ. Phys. Soc. Jpn.199867618221998JPSJ...67.1822O10.1143/JPSJ.67.1822 IsoshimaTMachidaKOhmiTPhys. Rev. A199960648571999PhRvA..60.4857I10.1103/PhysRevA.60.4857 SinatraADornstetterJ CCastinYFront. Phys.2012718610.1007/s11467-011-0219-7 HoT LPhys. Rev. Lett.19988147421998PhRvL..81..742H10.1103/PhysRevLett.81.742 KempenE G M vKokkelmansS J J M FHeinzenD JVerhaarB JPhys. Rev. Lett.20028890932012002PhRvL..88i3201V10.1103/PhysRevLett.88.093201 NistazakisH EFrantzeskakisD JKevrekidisP GMalomedB ACarretero-GonzlezRPhys. Rev. A20087730336122008PhRvA..77c3612N10.1103/PhysRevA.77.033612 MuellerE JPhys. Rev. A200469303360621119142004PhRvA..69c3606M10.1103/PhysRevA.69.033606 LiaoS JCommun. Nonlinear Sci. Numer. Simul.2010158200325926132010CNSNS..15.2003L1222.6508810.1016/j.cnsns.2009.09.002 WangD SHuX HHuJ PLiuW MPhys. Rev. A201081202560426066892010PhRvA..81b5604W10.1103/PhysRevA.81.025604 BaoW ZZhangY ZMethods Appl. Anal.2010174927351001206.35225 WangD SSongS WXiongBLiuW MPhys. Rev. A20118450536072011PhRvA..84e3607W10.1103/PhysRevA.84.053607 SzańkowskiPTrippenbachMInfeldERowlandsGPhys. Rev. A2011830136262011PhRvA..83a3626S10.1103/PhysRevA.83.013626 DionCMCancèsEPhys. Rev. E20036740467062003PhRvE..67d6706D10.1103/PhysRevE.67.046706 ChangM SHamleyC DBarrettM DSauerJ AFortierK MZhangWYouLChapmanM SPhys. Rev. Lett.200492141404032004PhRvL..92n0403C10.1103/PhysRevLett.92.140403 LiaoS JHomotopy Analysis Method in Nonlinear Differential Equations2012BeijingSpringer & Higher Education Press1253.3500110.1007/978-3-642-25132-0 KevrekidisP GTheocharisGFrantzeskakisD JMalomedB APhys. Rev. Lett.200390232304012003PhRvL..90w0401K10.1103/PhysRevLett.90.230401 LiaoS JBeyond Perturbation: Introduction to Homotopy Analysis Method2003Boca RatonChapman & Hall/CRC Press10.1201/9780203491164 TurkyilmazogluMComput. Fluids20103957931242.7636810.1016/j.compfluid.2009.12.007 ShiY RYangH JActa Phys. Sin.2010596726626771224.35374 Stamper-KurnD MAndrewsM RChikkaturA PInouyeSMiesnerH JStengerJKetterleWPhys. Rev. Lett.1998801020271998PhRvL..80.2027S10.1103/PhysRevLett.80.2027 DionC MCancèsEComput. Phys. Commun.2007177107872007CoPhC.177..787D1196.8101710.1016/j.cpc.2007.04.007 TurkyilmazogluMInt. J. Mech. Sci.20105212173510.1016/j.ijmecsci.2010.09.007 Dabrowska-WüsterB JOstrovskayaE AAlexanderT JKivsharY SPhys. Rev. A20077520236172007PhRvA..75b3617D10.1103/PhysRevA.75.023617 SaitoHUedaMPhys. Rev. A20057220236102005PhRvA..72b3610S10.1103/PhysRevA.72.023610 LiaoS JCommun. Nonlinear Sci. Numer. Simul.200914498324689312009CNSNS..14..983L1221.6512610.1016/j.cnsns.2008.04.013 MotsaS SSibandaPShateyiSCommun. Nonl. Sci. Numer. Simulat.2010159229326027131222.6509010.1016/j.cnsns.2009.09.019 SibandaPMotsaS SMakukulaZInt. J. Numer. Method. H.20122214291967910.1108/09615531211188766 ShiY RXuX JWuZ XWangY HYangH JDuanW SLüK PActa Phys. Sin.20065515551202.65130 IedaJMiyakawaTWadatiMLaser Phys.20051646782006LaPhy..16..678I10.1134/S1054660X06040220 BaoW ZLimF YSIAM J. Sci. Comput.20083041925240714710.1137/070698488 WangD SHuX HLiuW MPhys. Rev. A201082202361226066892010PhRvA..82b3612W10.1103/PhysRevA.82.023612 ZhaoY LLinZ LLiuZLiaoS JAppl. Math. Comput.201221817836329213311245.6509910.1016/j.amc.2012.02.004 TurkyilmazogluMInt. J. Therm. Sci.201150583110.1016/j.ijthermalsci.2010.12.014 PappS BPinoJ MWiemanC EPhys. Rev. Lett.200810140404022008PhRvL.101d0402P10.1103/PhysRevLett.101.040402 LiaoS JInt. J. Non-linear Mech.20043922712004IJNLM..39..271L0513845010.1016/S0020-7462(02)00174-9 StengerJInouyeSStamper-KurnD MMiesnerH JChikkaturA PKetterleWNature199839667093451998Natur.396..345S10.1038/24567 TurkyilmazogluMInt. J. Nonlinear Sci. Numer. Simul.2011121–89 S. J. Liao, PhD Thesis, Shanghai Jiao Tong University, 1992 TurkyilmazogluMAppl. Math. Lett.20102310122626656011195.6510410.1016/j.aml.2010.06.003 X W Guan (332_CR5) 2012; 7 T L Ho (332_CR6) 1998; 81 A Sinatra (332_CR4) 2012; 7 S J Liao (332_CR25) 2012 S J Liao (332_CR24) 2003 S J Liao (332_CR28) 2009; 14 S S Motsa (332_CR41) 2010; 15 M Turkyilmazoglu (332_CR33) 2010; 23 Y Cheng (332_CR29) 2006; 47 S J Liao (332_CR27) 2010; 15 P Szańkowski (332_CR16) 2011; 83 H Saito (332_CR18) 2005; 72 M Turkyilmazoglu (332_CR34) 2010; 52 M Turkyilmazoglu (332_CR38) 2012; 17 P G Kevrekidis (332_CR9) 2003; 90 W Z Bao (332_CR20) 2008; 30 M Turkyilmazoglu (332_CR37) 2011; 12 T Ohmi (332_CR7) 1998; 67 T Isoshima (332_CR8) 1999; 60 M S Chang (332_CR3) 2004; 92 J Ieda (332_CR14) 2005; 16 D S Wang (332_CR21) 2011; 84 D S Wang (332_CR23) 2010; 81 B J Dabrowska-Wüster (332_CR15) 2007; 75 332_CR26 R Barnett (332_CR17) 2006; 97 S J Liao (332_CR30) 2004; 39 CM Dion (332_CR43) 2003; 67 M Turkyilmazoglu (332_CR35) 2010; 39 H E Nistazakis (332_CR12) 2008; 77 N N Klausen (332_CR10) 2001; 64 S B Papp (332_CR45) 2008; 101 J Stenger (332_CR1) 1998; 396 S J Liao (332_CR31) 2010; 15 Y R Shi (332_CR39) 2006; 55 D M Stamper-Kurn (332_CR2) 1998; 80 M Turkyilmazoglu (332_CR36) 2011; 50 W Z Bao (332_CR19) 2010; 17 D S Wang (332_CR22) 2010; 82 C M Dion (332_CR44) 2007; 177 E G M v Kempen (332_CR11) 2002; 88 P Sibanda (332_CR42) 2012; 22 E J Mueller (332_CR13) 2004; 69 Y L Zhao (332_CR32) 2012; 218 Y R Shi (332_CR40) 2010; 59 |
| References_xml | – reference: TurkyilmazogluMInt. J. Therm. Sci.201150583110.1016/j.ijthermalsci.2010.12.014 – reference: ShiY RYangH JActa Phys. Sin.2010596726626771224.35374 – reference: BaoW ZZhangY ZMethods Appl. Anal.2010174927351001206.35225 – reference: HoT LPhys. Rev. Lett.19988147421998PhRvL..81..742H10.1103/PhysRevLett.81.742 – reference: SzańkowskiPTrippenbachMInfeldERowlandsGPhys. Rev. A2011830136262011PhRvA..83a3626S10.1103/PhysRevA.83.013626 – reference: GuanX WFront. Phys.201271810.1007/s11467-011-0213-0 – reference: MuellerE JPhys. Rev. A200469303360621119142004PhRvA..69c3606M10.1103/PhysRevA.69.033606 – reference: S. J. Liao, PhD Thesis, Shanghai Jiao Tong University, 1992 – reference: TurkyilmazogluMCommun. Nonlinear Sci. Numer. Simul.20121711409729303092012CNSNS..17.4097T0608193410.1016/j.cnsns.2012.01.030 – reference: Stamper-KurnD MAndrewsM RChikkaturA PInouyeSMiesnerH JStengerJKetterleWPhys. Rev. Lett.1998801020271998PhRvL..80.2027S10.1103/PhysRevLett.80.2027 – reference: ZhaoY LLinZ LLiuZLiaoS JAppl. Math. Comput.201221817836329213311245.6509910.1016/j.amc.2012.02.004 – reference: TurkyilmazogluMAppl. Math. Lett.20102310122626656011195.6510410.1016/j.aml.2010.06.003 – reference: KevrekidisP GTheocharisGFrantzeskakisD JMalomedB APhys. Rev. Lett.200390232304012003PhRvL..90w0401K10.1103/PhysRevLett.90.230401 – reference: SinatraADornstetterJ CCastinYFront. Phys.2012718610.1007/s11467-011-0219-7 – reference: TurkyilmazogluMComput. Fluids20103957931242.7636810.1016/j.compfluid.2009.12.007 – reference: TurkyilmazogluMInt. J. Mech. Sci.20105212173510.1016/j.ijmecsci.2010.09.007 – reference: WangD SSongS WXiongBLiuW MPhys. Rev. A20118450536072011PhRvA..84e3607W10.1103/PhysRevA.84.053607 – reference: KlausenN NBohnJ LGreeneC HPhys. Rev. A20016450536022001PhRvA..64e3602K10.1103/PhysRevA.64.053602 – reference: LiaoS JBeyond Perturbation: Introduction to Homotopy Analysis Method2003Boca RatonChapman & Hall/CRC Press10.1201/9780203491164 – reference: MotsaS SSibandaPShateyiSCommun. Nonl. Sci. Numer. Simulat.2010159229326027131222.6509010.1016/j.cnsns.2009.09.019 – reference: LiaoS JHomotopy Analysis Method in Nonlinear Differential Equations2012BeijingSpringer & Higher Education Press1253.3500110.1007/978-3-642-25132-0 – reference: LiaoS JCommun. Nonlinear Sci. Numer. Simul.2010158200325926132010CNSNS..15.2003L1222.6508810.1016/j.cnsns.2009.09.002 – reference: NistazakisH EFrantzeskakisD JKevrekidisP GMalomedB ACarretero-GonzlezRPhys. Rev. A20087730336122008PhRvA..77c3612N10.1103/PhysRevA.77.033612 – reference: IsoshimaTMachidaKOhmiTPhys. Rev. A199960648571999PhRvA..60.4857I10.1103/PhysRevA.60.4857 – reference: ShiY RXuX JWuZ XWangY HYangH JDuanW SLüK PActa Phys. Sin.20065515551202.65130 – reference: IedaJMiyakawaTWadatiMLaser Phys.20051646782006LaPhy..16..678I10.1134/S1054660X06040220 – reference: PappS BPinoJ MWiemanC EPhys. Rev. Lett.200810140404022008PhRvL.101d0402P10.1103/PhysRevLett.101.040402 – reference: SibandaPMotsaS SMakukulaZInt. J. Numer. Method. H.20122214291967910.1108/09615531211188766 – reference: DionCMCancèsEPhys. Rev. E20036740467062003PhRvE..67d6706D10.1103/PhysRevE.67.046706 – reference: BaoW ZLimF YSIAM J. Sci. Comput.20083041925240714710.1137/070698488 – reference: Dabrowska-WüsterB JOstrovskayaE AAlexanderT JKivsharY SPhys. Rev. A20077520236172007PhRvA..75b3617D10.1103/PhysRevA.75.023617 – reference: StengerJInouyeSStamper-KurnD MMiesnerH JChikkaturA PKetterleWNature199839667093451998Natur.396..345S10.1038/24567 – reference: KempenE G M vKokkelmansS J J M FHeinzenD JVerhaarB JPhys. Rev. Lett.20028890932012002PhRvL..88i3201V10.1103/PhysRevLett.88.093201 – reference: TurkyilmazogluMInt. J. Nonlinear Sci. Numer. Simul.2011121–89 – reference: ChangM SHamleyC DBarrettM DSauerJ AFortierK MZhangWYouLChapmanM SPhys. Rev. Lett.200492141404032004PhRvL..92n0403C10.1103/PhysRevLett.92.140403 – reference: OhmiTMachidaKJ. Phys. Soc. Jpn.199867618221998JPSJ...67.1822O10.1143/JPSJ.67.1822 – reference: BarnettRTurnerADemlerEPhys. Rev. Lett.200697181804122006PhRvL..97r0412B10.1103/PhysRevLett.97.180412 – reference: WangD SHuX HHuJ PLiuW MPhys. Rev. A201081202560426066892010PhRvA..81b5604W10.1103/PhysRevA.81.025604 – reference: ChengYLiaoS JCommun. Nonlinear Sci. Numer. Simul.20064775 – reference: LiaoS JCommun. Nonlinear Sci. Numer. Simul.200914498324689312009CNSNS..14..983L1221.6512610.1016/j.cnsns.2008.04.013 – reference: DionC MCancèsEComput. Phys. Commun.2007177107872007CoPhC.177..787D1196.8101710.1016/j.cpc.2007.04.007 – reference: WangD SHuX HLiuW MPhys. Rev. A201082202361226066892010PhRvA..82b3612W10.1103/PhysRevA.82.023612 – reference: LiaoS JInt. J. Non-linear Mech.20043922712004IJNLM..39..271L0513845010.1016/S0020-7462(02)00174-9 – reference: SaitoHUedaMPhys. Rev. A20057220236102005PhRvA..72b3610S10.1103/PhysRevA.72.023610 – volume: 82 start-page: 023612 issue: 2 year: 2010 ident: 332_CR22 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.82.023612 – volume: 67 start-page: 1822 issue: 6 year: 1998 ident: 332_CR7 publication-title: J. Phys. Soc. Jpn. doi: 10.1143/JPSJ.67.1822 – volume: 14 start-page: 983 issue: 4 year: 2009 ident: 332_CR28 publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2008.04.013 – volume: 15 start-page: 2003 issue: 8 year: 2010 ident: 332_CR27 publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2009.09.002 – volume: 72 start-page: 023610 issue: 2 year: 2005 ident: 332_CR18 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.72.023610 – volume: 47 start-page: 75 year: 2006 ident: 332_CR29 publication-title: Commun. Nonlinear Sci. Numer. Simul. – volume: 60 start-page: 4857 issue: 6 year: 1999 ident: 332_CR8 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.60.4857 – volume: 77 start-page: 033612 issue: 3 year: 2008 ident: 332_CR12 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.77.033612 – volume: 15 start-page: 2003 issue: 8 year: 2010 ident: 332_CR31 publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2009.09.002 – volume: 69 start-page: 033606 issue: 3 year: 2004 ident: 332_CR13 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.69.033606 – volume: 88 start-page: 093201 issue: 9 year: 2002 ident: 332_CR11 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.88.093201 – volume: 30 start-page: 1925 issue: 4 year: 2008 ident: 332_CR20 publication-title: SIAM J. Sci. Comput. doi: 10.1137/070698488 – volume: 22 start-page: 4 issue: 1 year: 2012 ident: 332_CR42 publication-title: Int. J. Numer. Method. H. doi: 10.1108/09615531211188766 – volume: 17 start-page: 4097 issue: 11 year: 2012 ident: 332_CR38 publication-title: Commun. Nonlinear Sci. Numer. Simul. doi: 10.1016/j.cnsns.2012.01.030 – volume-title: Homotopy Analysis Method in Nonlinear Differential Equations year: 2012 ident: 332_CR25 doi: 10.1007/978-3-642-25132-0 – volume: 52 start-page: 1735 issue: 12 year: 2010 ident: 332_CR34 publication-title: Int. J. Mech. Sci. doi: 10.1016/j.ijmecsci.2010.09.007 – volume: 7 start-page: 8 issue: 1 year: 2012 ident: 332_CR5 publication-title: Front. Phys. doi: 10.1007/s11467-011-0213-0 – volume: 81 start-page: 025604 issue: 2 year: 2010 ident: 332_CR23 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.81.025604 – volume: 218 start-page: 8363 issue: 17 year: 2012 ident: 332_CR32 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2012.02.004 – volume: 177 start-page: 787 issue: 10 year: 2007 ident: 332_CR44 publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2007.04.007 – volume-title: Beyond Perturbation: Introduction to Homotopy Analysis Method year: 2003 ident: 332_CR24 doi: 10.1201/9780203491164 – volume: 23 start-page: 1226 issue: 10 year: 2010 ident: 332_CR33 publication-title: Appl. Math. Lett. doi: 10.1016/j.aml.2010.06.003 – ident: 332_CR26 – volume: 59 start-page: 67 year: 2010 ident: 332_CR40 publication-title: Acta Phys. Sin. doi: 10.7498/aps.59.67 – volume: 16 start-page: 678 issue: 4 year: 2005 ident: 332_CR14 publication-title: Laser Phys. doi: 10.1134/S1054660X06040220 – volume: 84 start-page: 053607 issue: 5 year: 2011 ident: 332_CR21 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.84.053607 – volume: 92 start-page: 140403 issue: 14 year: 2004 ident: 332_CR3 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.92.140403 – volume: 83 start-page: 013626 year: 2011 ident: 332_CR16 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.83.013626 – volume: 80 start-page: 2027 issue: 10 year: 1998 ident: 332_CR2 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.80.2027 – volume: 101 start-page: 040402 issue: 4 year: 2008 ident: 332_CR45 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.101.040402 – volume: 64 start-page: 053602 issue: 5 year: 2001 ident: 332_CR10 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.64.053602 – volume: 396 start-page: 345 issue: 6709 year: 1998 ident: 332_CR1 publication-title: Nature doi: 10.1038/24567 – volume: 12 start-page: 9 issue: 1–8 year: 2011 ident: 332_CR37 publication-title: Int. J. Nonlinear Sci. Numer. Simul. doi: 10.1515/ijnsns.2011.020 – volume: 90 start-page: 230401 issue: 23 year: 2003 ident: 332_CR9 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.90.230401 – volume: 39 start-page: 271 issue: 2 year: 2004 ident: 332_CR30 publication-title: Int. J. Non-linear Mech. doi: 10.1016/S0020-7462(02)00174-9 – volume: 81 start-page: 742 issue: 4 year: 1998 ident: 332_CR6 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.81.742 – volume: 75 start-page: 023617 issue: 2 year: 2007 ident: 332_CR15 publication-title: Phys. Rev. A doi: 10.1103/PhysRevA.75.023617 – volume: 39 start-page: 793 issue: 5 year: 2010 ident: 332_CR35 publication-title: Comput. Fluids doi: 10.1016/j.compfluid.2009.12.007 – volume: 7 start-page: 86 issue: 1 year: 2012 ident: 332_CR4 publication-title: Front. Phys. doi: 10.1007/s11467-011-0219-7 – volume: 97 start-page: 180412 issue: 18 year: 2006 ident: 332_CR17 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.97.180412 – volume: 17 start-page: 49 year: 2010 ident: 332_CR19 publication-title: Methods Appl. Anal. doi: 10.4310/MAA.2010.v17.n1.a2 – volume: 15 start-page: 2293 issue: 9 year: 2010 ident: 332_CR41 publication-title: Commun. Nonl. Sci. Numer. Simulat. doi: 10.1016/j.cnsns.2009.09.019 – volume: 67 start-page: 046706 issue: 4 year: 2003 ident: 332_CR43 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.67.046706 – volume: 50 start-page: 831 issue: 5 year: 2011 ident: 332_CR36 publication-title: Int. J. Therm. Sci. doi: 10.1016/j.ijthermalsci.2010.12.014 – volume: 55 start-page: 1555 year: 2006 ident: 332_CR39 publication-title: Acta Phys. Sin. doi: 10.7498/aps.55.1555 |
| SSID | ssj0001174462 |
| Score | 1.902121 |
| Snippet | The homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions for the Gross-Pitaevskii equations, a set of nonlinear... |
| SourceID | proquest crossref springer higheredpress chongqing |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 319 |
| SubjectTerms | analytical solution Astronomy Astrophysics and Cosmology Atomic Atomic interactions Bose-Einstein condensates Condensed Matter Physics Exact solutions Galerkin谱方法 Gross-Pitaevskii equation homotopy analysis method Homotopy theory Molecular Optical and Plasma Physics Particle and Nuclear Physics Physics Physics and Astronomy Research Article Schrodinger equation Spectral methods spin-1 Bose-Einstein condensate 势阱 同伦分析 爱因斯坦凝聚 玻色 自旋 谐振 近似解析解 |
| SummonAdditionalLinks | – databaseName: SpringerLINK - Czech Republic Consortium dbid: AGYKE link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8QwEB5kRRDEt7i-yMGTUmmapKZHFR8o6kVBTyHJproo3dVWEH-9k2y764oK3lqapCQzmXyTTL4B2LZM61zyPNp3PPUOio2kRmNojeEZdT523F8UvrxKz275-Z24q-9xl020e3MkGSz16LJbmNQhGwFjSYTAcVJQmckWTB6c3l982VpBlM1DKtEk9veP8bk5z_ypHc-q8NgrHl7wn2Or08xjCLVwnRCSOgZBv52ahsXoZA5umm4MYlCe9t4qs2c_vjE8_rOf8zBbg1NyMNCmBZhwxSJMhSBRWy7BdWAwCZvfZKiyBFEvQRRJyn63iCg57JUuOu4i6nTdgqC3jYatREBL8E0TT5TtyXhJ9ar7y3B7cnxzdBbVCRkiyzJaRc5kkuaMMyudZTJHT1YIh2K1IubaOaolroSJ4YZJIdIs1dzm0to4R9SDyIKtQKvoFW4ViHSsk_J9zUTGuKYxlvRMg6npZLER1rZhbSgU1R8QbygUpD9mFG2IGykpW1OZ-4waz2pEwuwHUeEgKj-I6r0NO8MqTXN_FKZjole5J5Pwqcn_qrPRqIeqzUCpkox6j5GltA27jbRHn39tbO1fpddhOhkk6UCt2YBW9frmNhEqVWarnhqfvLUH4w priority: 102 providerName: Springer Nature |
| Title | Analytical solutions for the spin-1 Bose-Einstein condensate in a harmonic trap |
| URI | http://lib.cqvip.com/qk/71009X/201303/46243725.html https://journal.hep.com.cn/fop/EN/10.1007/s11467-013-0332-x https://link.springer.com/article/10.1007/s11467-013-0332-x https://www.proquest.com/docview/2918626361 |
| Volume | 8 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LSwMxEA4-LoKIomK1Sg6elOBmk6zZk1RpFcUHYkFPIZtmtSDb2q3gz3cm3W2pYE_7SnLIzM58yUy-IeTYCWtzLXN27mWCCxTHtAVj6LJMptxj7jgeFL5_SG668vZVvVYbbmWVVlnbxGCoewOHe-RnccoRfIuEXwy_GFaNwuhqVUJjmaxy8DSo57pzPdtjAbgtQ03ROMKDyHBfBzbD6blgJUJ5AyFi9oP0Ch-D4v0LnMacm1r_CDkXvhdyU-ew6J_wafBKnU2yUcFJ2prIf4ss-WKbPAamkbBJTaeqRQGdUkB7tBz2C8bp5aD0rN0HdOj7BYVVMRigEoAnhSdLkdAaSXPpeGSHO6Tbab9c3bCqcAJzIuVj5rNU81xI4bR3Quew4lTKw_Q7FUnrPbcaPFacyUxopZI0sdLl2rkoB3QCCEDskpViUPg9QrUXvUSeW6FSIS2PoCUyAiZZL40y5VyD7E_nzAwnBBkG5hnDgapBonoSjasox7HyxaeZkSWjDAzIwKAMzE-DnEy71MMtaMznJGNyJH3AEuKL-jRr6Znqdy3NTLka5LSW6Ozzv4PtLx7sgKzFk-oZoGVNsjIefftDwDDj7Cgo6hFZbV2_3bXhetl-eHqGt9249QvhTO7j |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3fT9swED6x8rBJCA1t08qPzQ_sZZO1OHaC84DQ2IrKgG6aQOLNc1wHKqG0kE6Df4q_kTs3aVUk-sZbojhWdHe5--zzfQew7aS1hVYF3_EqpQWK49qiM3R5rjLh6ew4FQqf9NLumfp5npwvwX1TC0PHKhufGBx1f-hoj_xrnAkC3zIVe6NrTl2jKLvatNCYmMWRv_uPS7Zq9_AH6vdTHB90Tr93ed1VgDuZiTH3eaZFIZV02jupC1yOJYnHb3NJpKz3wmp053GucqmTJM1Sq1yhnYsKDN0YHiXO-wKWFVW0tmB5v9P7_We2q4MAX4UupnFEpc943aRSQ71e8EuhoYKUMb8lQofLYXlxjWFqLjCuXIZTHr4fTsPOod9HCdsQBw9ew2oNYNm3icWtwZIv38CvwG0StsXZ1JgZ4mGG-JJVo0HJBdsfVp53BohH_aBkuA5Hl1ch1GV4ZxlRaBNNLxvf2NFbOHsWob6DVjks_Xtg2st-qnYsylcqKyIcSRyEad7Pojxxrg3rU5mZ0YSSw6CcKQGZtCFqhGhcTXJOvTauzIyemXRgUAeGdGBu2_B5-koz3YLBYk4zpiCaCWpavuidzUZ7pnYQlZmZcxu-NBqdPX5ysvXFk32El93Tk2NzfNg72oBX8aR3B1rcJrTGN__8FiKocf6hNlsGf5_7T3kAWFEo7A |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3dS8MwEA-iKIKInzg_8-CTUmyapEsf58fwWx8c-BbSLHUD6aat4J_vXdZuTFTwraVJCneX5Jfc3e8IObTcmEyJLGg6EeMBxQbKwGJo01QkzGHsOCYK393Hlx1x_SyfqzqnRR3tXrskRzkNyNKUlyfDbnYySXzzE9xXJuA8CgBEzsFqzNDQO1FrcskCeFv4oqJRiJnI8Fx7Nn8aBfkVeoP85Q3-PrVPLfV80IXr-uDUKTD6zX_qt6X2Clmu8CRtjQxglcy4fI3M-7hOW6yTB0864u-r6djKKABVCsCPFsN-HjB6OihccNEHoOj6OQVJwFpUAAal8GYoclsjfy4t381wg3TaF09nl0FVQyGwPGFl4NJEsYwLbpWzXGVw-JTSgSasDIVxjhkFm1eUipQrKeMkNsJmytowA6ACYIBvktl8kLstQpXj3Vg0DZcJF4aF0BLJAeO0m4SptLZBtsfS08MRV4YGiaNnUDZIWItT24p9HItgvOoJbzJqQ4M2NGpDfzbI0bhLPdwfjdmUjnSG_A9YTfyvPru1HnU1cwsdJQwPeTxmDXJc63by-dfBtv_V-oAsPJ639e3V_c0OWYxGJTbAEnfJbPn-4fYA6JTpvjfmL--e8e8 |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Analytical+solutions+for+the+spin-1+Bose-Einstein+condensate+in+a+harmonic+trap&rft.jtitle=Frontiers+of+physics&rft.au=Shi%2C+Yu-Ren&rft.au=Wang%2C+Xue-Ling&rft.au=Wang%2C+Guang-Hui&rft.au=Liu%2C+Cong-Bo&rft.date=2013-06-01&rft.pub=Springer+Nature+B.V&rft.issn=2095-0462&rft.eissn=2095-0470&rft.volume=8&rft.issue=3&rft.spage=319&rft.epage=327&rft_id=info:doi/10.1007%2Fs11467-013-0332-x |
| thumbnail_s | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=http%3A%2F%2Fimage.cqvip.com%2Fvip1000%2Fqk%2F71009X%2F71009X.jpg |