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Article: Exact solutions for periodic and solitary matter waves in nonlinear lattices

TitleExact solutions for periodic and solitary matter waves in nonlinear lattices
Authors
KeywordsGross-Pitaevskii equation
Nonlinear Schrödinger equation
Optical lattice
Elliptic functions
Cnoidal waves
Issue Date2011
PublisherAmerican Institute of Mathematical Sciences. The Journal's web site is located at https://www.aimsciences.org/journals/home.jsp?journalID=15
Citation
Discrete and Continuous Dynamical Systems: Series S, 2011, v. 4 n. 5, p. 1299-1325 How to Cite?
AbstractWe produce three vast classes of exact periodic and solitonic solutions to the one-dimensional Gross-Pitaevskii equation (GPE) with the pseudopotential in the form of a nonlinear lattice (NL), induced by a spatially periodic modulation of the local nonlinearity. It is well known that NLs in Bose-Einstein condensates (BECs) may be created by means of the Feshbach-resonance technique. The model may also include linear potentials with the same periodicity. The NL modulation function, the linear potential (if any), and the corresponding exact solutions are expressed in terms of the Jacobi's elliptic functions of three types, cn, dn, and sn, which give rise to the three different classes of the solutions. The potentials and associated solutions are parameterized by two free constants and an additional sign parameter in the absence of the linear potential. In the presence of the latter, the solution families feature two additional free parameters. The families include both sign-constant and sign-changing NLs. Density maxima of the solutions may coincide with either minima or maxima of the periodic pseudopotential. The solutions reduce to solitons in the limit of the infinite period. The stability of the solutions is tested via systematic direct simulations of the GPE. As a result, stability regions are identified for the periodic solutions and solitons. The periodic patterns of cn type, and the respective limit-form solutions in the form of bright solitons, may be stable both in the absence and presence of the linear potential. On the contrary, the stability of the two other solution classes, of the dn and sn types, is only possible with the linear potential.
Persistent Identifierhttp://hdl.handle.net/10722/207879
ISSN
2015 Impact Factor: 0.737
2015 SCImago Journal Rankings: 0.683

 

DC FieldValueLanguage
dc.contributor.authorTsang, CH-
dc.contributor.authorMalomed, BA-
dc.contributor.authorChow, KW-
dc.date.accessioned2015-01-20T07:11:52Z-
dc.date.available2015-01-20T07:11:52Z-
dc.date.issued2011-
dc.identifier.citationDiscrete and Continuous Dynamical Systems: Series S, 2011, v. 4 n. 5, p. 1299-1325-
dc.identifier.issn1937-1632-
dc.identifier.urihttp://hdl.handle.net/10722/207879-
dc.description.abstractWe produce three vast classes of exact periodic and solitonic solutions to the one-dimensional Gross-Pitaevskii equation (GPE) with the pseudopotential in the form of a nonlinear lattice (NL), induced by a spatially periodic modulation of the local nonlinearity. It is well known that NLs in Bose-Einstein condensates (BECs) may be created by means of the Feshbach-resonance technique. The model may also include linear potentials with the same periodicity. The NL modulation function, the linear potential (if any), and the corresponding exact solutions are expressed in terms of the Jacobi's elliptic functions of three types, cn, dn, and sn, which give rise to the three different classes of the solutions. The potentials and associated solutions are parameterized by two free constants and an additional sign parameter in the absence of the linear potential. In the presence of the latter, the solution families feature two additional free parameters. The families include both sign-constant and sign-changing NLs. Density maxima of the solutions may coincide with either minima or maxima of the periodic pseudopotential. The solutions reduce to solitons in the limit of the infinite period. The stability of the solutions is tested via systematic direct simulations of the GPE. As a result, stability regions are identified for the periodic solutions and solitons. The periodic patterns of cn type, and the respective limit-form solutions in the form of bright solitons, may be stable both in the absence and presence of the linear potential. On the contrary, the stability of the two other solution classes, of the dn and sn types, is only possible with the linear potential.-
dc.languageeng-
dc.publisherAmerican Institute of Mathematical Sciences. The Journal's web site is located at https://www.aimsciences.org/journals/home.jsp?journalID=15-
dc.relation.ispartofDiscrete and Continuous Dynamical Systems: Series S-
dc.rightsDiscrete and Continuous Dynamical Systems: Series S. Copyright © American Institute of Mathematical Sciences.-
dc.rightsThis is a pre-copy-editing, author-produced PDF of an article accepted for publication in [insert journal title] following peer review. The definitive publisher-authenticated version [insert complete citation information here] is available online at: xxxxxxx [insert URL that the author will receive upon publication here].-
dc.subjectGross-Pitaevskii equation-
dc.subjectNonlinear Schrödinger equation-
dc.subjectOptical lattice-
dc.subjectElliptic functions-
dc.subjectCnoidal waves-
dc.titleExact solutions for periodic and solitary matter waves in nonlinear latticesen_US
dc.typeArticleen_US
dc.identifier.emailTsang, CH: alantsangch@yahoo.com.hk-
dc.identifier.emailChow, KW: kwchow@hku.hk-
dc.identifier.doi10.3934/dcdss.2011.4.1299-
dc.identifier.hkuros170644-
dc.identifier.volume4-
dc.identifier.issue5-
dc.identifier.spage1299-
dc.identifier.epage1325-
dc.publisher.placeUnited States-

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