A Cylindrical Bose-Einstein Condensate
Calculation of Solitary Waves
Stavros Komineas Nikos Papanicolaou
Cavendish Laboratory University of Crete and
University of Cambridge, U.K. Research Center of Crete (FORTH), Greece

Introduction
The purpose of this page is to make publicly available the numerical solution for vortex rings in a cylindrical BEC.
We consider solitary waves in a BEC confined through a harmonic potential in the cylindrical geometry of the figure. If the cylinder is infinitely elongated in the z direction they have the form:


The wave function satisfies the equation:



$\gamma = \nu a$




The cylindrical geometry
Results and wave functions
In the files given below each line contains the coordinates and the wave function in the following order: , . Coupling constant
We have three sequences of solitary waves shown on the
energy-momentum (E-Q) dispersion.
Sequence I
(1) v=1.0 wave function (graph)
(2) v=0.6 wave function (graph)
(3) v=0.0 wave function (graph)
(4) v=-0.8 wave function (graph)


Sequence II
Obtained from sequence I through the relation
$v\to -v,\; \Psi\to\Psi^*$

Sequence III
(1) v=0.4 wave function (graph)
(2) v=0.0 wave function (graph)
(3) v=-0.4 wave function (graph)

$v = \frac{dE}{dQ}$
References
[1] S. Komineas and N. Papanicolaou, "Vortex Rings and Lieb Modes in a Cylindrical BEC", Phys. Rev. Lett. 89, 070402 (2002)
[2] S. Komineas and N. Papanicolaou, "Nonlinear waves in a Cylindrical BEC", Phys. Rev. A 67, 023615 (2003)
[3] S. Komineas and N. Papanicolaou, "Solitons, solitonic vortices, and vortex rings in a Cylindrical BEC" , Phys. Rev. A 68, 043617 (2003)