Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice
We present two new families of stationary solutions for equations of Bose-Fermi mixtures with an elliptic function potential with modulus k. We also discuss particular cases when the quasiperiodic solutions become periodic ones. In the limit of a sinusoidal potential (k → 0) our solutions model a qu...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2007 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2007
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147363 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice / N.A. Kostov, V.S. Gerdjikov, T.I. Valchev // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 27 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862639931060387840 |
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| author | Kostov, N.A. Gerdjikov, V.S. Valchev, T.I. |
| author_facet | Kostov, N.A. Gerdjikov, V.S. Valchev, T.I. |
| citation_txt | Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice / N.A. Kostov, V.S. Gerdjikov, T.I. Valchev // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 27 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We present two new families of stationary solutions for equations of Bose-Fermi mixtures with an elliptic function potential with modulus k. We also discuss particular cases when the quasiperiodic solutions become periodic ones. In the limit of a sinusoidal potential (k → 0) our solutions model a quasi-one dimensional quantum degenerate Bose-Fermi mixture trapped in optical lattice. In the limit k → 1 the solutions are expressed by hyperbolic function solutions (vector solitons). Thus we are able to obtain in an unified way quasi-periodic and periodic waves, and solitons. The precise conditions for existence of every class of solutions are derived. There are indications that such waves and localized objects may be observed in experiments with cold quantum degenerate gases.
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| first_indexed | 2025-12-01T02:21:47Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-147363 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T02:21:47Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kostov, N.A. Gerdjikov, V.S. Valchev, T.I. 2019-02-14T14:44:05Z 2019-02-14T14:44:05Z 2007 Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice / N.A. Kostov, V.S. Gerdjikov, T.I. Valchev // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 27 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37K20; 35Q51; 74J30; 78A60 https://nasplib.isofts.kiev.ua/handle/123456789/147363 We present two new families of stationary solutions for equations of Bose-Fermi mixtures with an elliptic function potential with modulus k. We also discuss particular cases when the quasiperiodic solutions become periodic ones. In the limit of a sinusoidal potential (k → 0) our solutions model a quasi-one dimensional quantum degenerate Bose-Fermi mixture trapped in optical lattice. In the limit k → 1 the solutions are expressed by hyperbolic function solutions (vector solitons). Thus we are able to obtain in an unified way quasi-periodic and periodic waves, and solitons. The precise conditions for existence of every class of solutions are derived. There are indications that such waves and localized objects may be observed in experiments with cold quantum degenerate gases. The present work is supported by the National Science Foundation of Bulgaria, contract No F-1410. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice Article published earlier |
| spellingShingle | Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice Kostov, N.A. Gerdjikov, V.S. Valchev, T.I. |
| title | Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice |
| title_full | Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice |
| title_fullStr | Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice |
| title_full_unstemmed | Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice |
| title_short | Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice |
| title_sort | exact solutions for equations of bose-fermi mixtures in one-dimensional optical lattice |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147363 |
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