  We consider the ground state of an attractively-interacting atomic
Bose-Einstein condensate in a prolate, cylindrically symmetric harmonic trap.
If a true quasi-one-dimensional limit is realized, then for sufficiently weak
axial trapping this ground state takes the form of a bright soliton solution of
the nonlinear Schroedinger equation. Using analytic variational and highly
accurate numerical solutions of the Gross-Pitaevskii equation we systematically
and quantitatively assess how soliton-like this ground state is, over a wide
range of trap and interaction strengths. Our analysis reveals that the regime
in which the ground state is highly soliton-like is significantly restricted,
and occurs only for experimentally challenging trap anisotropies. This result,
and our broader identification of regimes in which the ground state is
well-approximated by our simple analytic variational solution, are relevant to
a range of potential experiments involving attractively-interacting
Bose-Einstein condensates.
