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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2007 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | 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 |
| Цитувати: | 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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nasplib_isofts_kiev_ua-123456789-147363 |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice |
| spellingShingle |
Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice Kostov, N.A. Gerdjikov, V.S. Valchev, T.I. |
| title_short |
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_sort |
exact solutions for equations of bose-fermi mixtures in one-dimensional optical lattice |
| author |
Kostov, N.A. Gerdjikov, V.S. Valchev, T.I. |
| author_facet |
Kostov, N.A. Gerdjikov, V.S. Valchev, T.I. |
| publishDate |
2007 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147363 |
| 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. |
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2025-12-01T02:21:47Z |
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2025-12-01T02:21:47Z |
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