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Article: Exact solutions for periodic and solitary matter waves in nonlinear lattices
Title | Exact solutions for periodic and solitary matter waves in nonlinear lattices |
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Authors | |
Keywords | Gross-Pitaevskii equation Nonlinear Schrödinger equation Optical lattice Elliptic functions Cnoidal waves |
Issue Date | 2011 |
Publisher | American 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? |
Abstract | We 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 Identifier | http://hdl.handle.net/10722/207879 |
ISSN | 2023 Impact Factor: 1.3 2023 SCImago Journal Rankings: 0.541 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Tsang, CH | - |
dc.contributor.author | Malomed, BA | - |
dc.contributor.author | Chow, KW | - |
dc.date.accessioned | 2015-01-20T07:11:52Z | - |
dc.date.available | 2015-01-20T07:11:52Z | - |
dc.date.issued | 2011 | - |
dc.identifier.citation | Discrete and Continuous Dynamical Systems: Series S, 2011, v. 4 n. 5, p. 1299-1325 | - |
dc.identifier.issn | 1937-1632 | - |
dc.identifier.uri | http://hdl.handle.net/10722/207879 | - |
dc.description.abstract | We 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.language | eng | - |
dc.publisher | American Institute of Mathematical Sciences. The Journal's web site is located at https://www.aimsciences.org/journals/home.jsp?journalID=15 | - |
dc.relation.ispartof | Discrete and Continuous Dynamical Systems: Series S | - |
dc.subject | Gross-Pitaevskii equation | - |
dc.subject | Nonlinear Schrödinger equation | - |
dc.subject | Optical lattice | - |
dc.subject | Elliptic functions | - |
dc.subject | Cnoidal waves | - |
dc.title | Exact solutions for periodic and solitary matter waves in nonlinear lattices | en_US |
dc.type | Article | en_US |
dc.identifier.email | Tsang, CH: alantsangch@yahoo.com.hk | - |
dc.identifier.email | Chow, KW: kwchow@hku.hk | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.3934/dcdss.2011.4.1299 | - |
dc.identifier.scopus | eid_2-s2.0-80051535406 | - |
dc.identifier.hkuros | 170644 | - |
dc.identifier.volume | 4 | - |
dc.identifier.issue | 5 | - |
dc.identifier.spage | 1299 | - |
dc.identifier.epage | 1325 | - |
dc.identifier.isi | WOS:000214301400026 | - |
dc.publisher.place | United States | - |
dc.identifier.issnl | 1937-1179 | - |