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.
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