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SIGMA 3 (2007), 071, 14 pages nlin.SI/0703057
https://doi.org/10.3842/SIGMA.2007.071
Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice
Nikolay A. Kostov a, Vladimir S. Gerdjikov b and Tihomir I. Valchev b
a) Institute of Electronics, Bulgarian Academy of
Sciences, 72 Tsarigradsko chaussee, 1784 Sofia, Bulgaria
b) Institute for Nuclear Research and Nuclear
Energy, Bulgarian Academy of Sciences, 72 Tsarigradsko chaussee,
1784 Sofia, Bulgaria
Received March 30, 2007, in final form May
17, 2007; Published online May 30, 2007
Abstract
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.
Key words:
Bose-Fermi mixtures; one dimensional optical lattice.
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