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Article: Singular nonlinearity management for matter-wave solitons in normal and inverted parabolic potentials

TitleSingular nonlinearity management for matter-wave solitons in normal and inverted parabolic potentials
Authors
KeywordsGross-Pitaevskii Equation
Hirota Bilinear Method
Solitons
Issue Date2006
PublisherInstitute of Pure and Applied Physics. The Journal's web site is located at http://www.ipap.jp/jpsj/index.htm
Citation
Journal Of The Physical Society Of Japan, 2006, v. 75 n. 11 How to Cite?
AbstractWe produce a class of solvable Gross-Pitaevskii equations (GPEs), which incorporate the nonlinearity management, a time-dependent factor in front of the cubic term, accounting for the Feshbach resonance in variable magnetic field applied to the Bose-Einstein condensate, and the trapping potential, which may be either static or time-dependent. The GPE is transformed into an equation with a constant nonlinearity coefficient and an additional time-dependent linear term. We present four examples of the nonlinearity-management scenarios which, in proper conjugation with the trapping potential, lead to solvable GPEs. In two cases, the potential is required in the inverted form, which may be a physically meaningful one. In all the cases, the solvable schemes are singular, with the corresponding nonlinearity-enhancement factor diverging at one or multiple moments of time. This singularity may be relevant to the Feshbach resonance. Solvable equations with the normal trapping potential feature multiple singularities (thus limiting the applicability of the GPE to a finite interval of time), while, with the inverted potential, the singularity occurs only at t = 0, validating the equations for 0 < t < ∞. Using the Hirota transform (HT), we construct bright solitons for all solvable cases, and demonstrate that higher-order solitons can be obtained too. Dark solitons are also found, in counterparts of the same models with self-repulsion. In comparison with the previous analysis, a crucial ingredient of the present method is finding the soliton's chirp. ©2006 The Physical Society of Japan.
Persistent Identifierhttp://hdl.handle.net/10722/156880
ISSN
2015 Impact Factor: 1.559
2015 SCImago Journal Rankings: 0.720
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChow, KWen_US
dc.contributor.authorMalomed, BAen_US
dc.contributor.authorXiong, Ben_US
dc.contributor.authorLiu, WMen_US
dc.date.accessioned2012-08-08T08:44:24Z-
dc.date.available2012-08-08T08:44:24Z-
dc.date.issued2006en_US
dc.identifier.citationJournal Of The Physical Society Of Japan, 2006, v. 75 n. 11en_US
dc.identifier.issn0031-9015en_US
dc.identifier.urihttp://hdl.handle.net/10722/156880-
dc.description.abstractWe produce a class of solvable Gross-Pitaevskii equations (GPEs), which incorporate the nonlinearity management, a time-dependent factor in front of the cubic term, accounting for the Feshbach resonance in variable magnetic field applied to the Bose-Einstein condensate, and the trapping potential, which may be either static or time-dependent. The GPE is transformed into an equation with a constant nonlinearity coefficient and an additional time-dependent linear term. We present four examples of the nonlinearity-management scenarios which, in proper conjugation with the trapping potential, lead to solvable GPEs. In two cases, the potential is required in the inverted form, which may be a physically meaningful one. In all the cases, the solvable schemes are singular, with the corresponding nonlinearity-enhancement factor diverging at one or multiple moments of time. This singularity may be relevant to the Feshbach resonance. Solvable equations with the normal trapping potential feature multiple singularities (thus limiting the applicability of the GPE to a finite interval of time), while, with the inverted potential, the singularity occurs only at t = 0, validating the equations for 0 < t < ∞. Using the Hirota transform (HT), we construct bright solitons for all solvable cases, and demonstrate that higher-order solitons can be obtained too. Dark solitons are also found, in counterparts of the same models with self-repulsion. In comparison with the previous analysis, a crucial ingredient of the present method is finding the soliton's chirp. ©2006 The Physical Society of Japan.en_US
dc.languageengen_US
dc.publisherInstitute of Pure and Applied Physics. The Journal's web site is located at http://www.ipap.jp/jpsj/index.htmen_US
dc.relation.ispartofJournal of the Physical Society of Japanen_US
dc.subjectGross-Pitaevskii Equationen_US
dc.subjectHirota Bilinear Methoden_US
dc.subjectSolitonsen_US
dc.titleSingular nonlinearity management for matter-wave solitons in normal and inverted parabolic potentialsen_US
dc.typeArticleen_US
dc.identifier.emailChow, KW:kwchow@hku.hken_US
dc.identifier.authorityChow, KW=rp00112en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1143/JPSJ.75.114004en_US
dc.identifier.scopuseid_2-s2.0-33847282568en_US
dc.identifier.hkuros128213-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33847282568&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume75en_US
dc.identifier.issue11en_US
dc.identifier.isiWOS:000242210200021-
dc.publisher.placeJapanen_US
dc.identifier.scopusauthoridChow, KW=13605209900en_US
dc.identifier.scopusauthoridMalomed, BA=35555126200en_US
dc.identifier.scopusauthoridXiong, B=36464616900en_US
dc.identifier.scopusauthoridLiu, WM=36068491700en_US

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