1105.5537 (P. A. Andreev et al.)

New bright-like soliton solution in quasi-one-dimensional BEC in third
order on interaction radius    [PDF]

P. A. Andreev, L. S. Kuzmenkov

Nonlinear Schrodinger equations and corresponding quantum hydrodynamic (QHD)
equations are widely used in studying ultracold boson-fermion mixtures and
superconductors. In this article, we showed that a more exact account for
interaction in Bose-Einstein condensate (BEC), compared with the
Gross-Pitaevskii (GP) approximation, leads to the existence of a new type of a
soliton. We used the first-principle set of equations of QHD in the third order
by the interaction radius (TOIR), which corresponds to the GP equation in a
first order by the interaction radius. The solution for the soliton in a form
of expression for the particle concentration is obtained analytically. The
conditions of existence of the soliton are studied; the solution is shown to
exist if the interaction between the solitons is repulsive. For the particle
concentration of 10^{12}-10^{14} sm^{-3} used experimentally for the BEC, the
solution exists if the scattering length is of the order of 1 \mu m, which can
be reached using the Feshbach resonance. It is one of the limit case of
existence of new solution. The corresponding scattering length decrease with
the increasing of concentration of particles. The investigation of effects in
the TOIR gives a more detail information on interaction potentials between the
atoms and can be used for a more detail investigation into the potential
structure.

View original: http://arxiv.org/abs/1105.5537