  The Bose-Einstein condensate (BEC) of a dilute gas of bosons is well
described by the three-dimensional Gross-Pitaevskii equation (3D GPE), that is
a nonlinear Schrodinger equation. By imposing a transverse confinement the BEC
can travel only in the cylindrical axial direction. We show that in this case
the BEC with attractive interaction admits a 3D bright soliton solution which
generalizes the text-book one, that is valid in the one-dimensional limit (1D
GPE). Contrary to the 1D case, the 3D bright soliton exists only below a
critical number of Bosons that depends on the extent of confinement. Finally,
we find that the 3D bright soliton collapses if its density excedes a critical
value. Our results are obtained by using a nonpolynomial Schrodinger equation
(NPSE), an effective one-dimensional equation derived from the 3D GPE.
