Nonlinear waves in a cylindrical Bose-Einstein condensate
S. Komineasa and N. Papanicolaoub aPhysikalisches Institut, Universität Bayreuth,
D-95440 Bayreuth, Germany bDepartment of Physics, University of Crete,
and Research Center of Crete, Heraklion, Greece
Abstract
We present a calculation of solitary waves propagating in a
steady state with constant velocity $v$ along a cigar-shaped
Bose-Einstein trap approximated as infinitely-elongated cylindrical.
For sufficiently weak couplings (densities) the main features
of the calculated solitons could be captured by effective one-dimensional (1D)
models. However, for stronger couplings of practical interest, the
relevant solitary waves are found to be hybrids of quasi-1D solitons
and 3D vortex rings. An interesting hierarchy of vortex rings
occurs as the effective coupling constant is increased through
a sequence of critical values.
The energy-momentum dispersion of the above structures is shown to
exhibit characteristics similar to a mode proposed sometime ago by Lieb
within a strictly 1D model, as well as some rotonlike features.