%0 Journal Article
%T Degenerate ground states and stability of spatial solitons in quasi-one-dimensional Bose-Einstein Condensates
%A A. M. Dikande
%J Physics
%D 2001
%I arXiv
%X By examining the bound-state spectra of transverse fluctuations about one-dimensional, spatially localized dark and bright soliton wavetrains of the Gross-Pitaevskii equation, it is established that the low-temperature ground states of repulsive and attractive quasi-one-dimensional Bose-Einstein condensates are degenerate. In the one-soliton limit, both ground states are shown to possess two distinct transverse fluctuation modes which can couple to the spatial soliton: the first involves zero-energy exchange, costing only the soliton shape dressing via uniform translation of its centre of mass. The second mode contributes in a negative energy for the repulsive case, but positive energy in the attractive case. This unstability of the repulsive spatial soliton against localized transverse fluctuation modes invalidates the Gross-Pitaevskii equation for stationary solitonic processes in repulsive 1D Bose-Einstein-Condensate systems.
%U http://arxiv.org/abs/cond-mat/0111418v1