  Within the framework of the mean-field description, we investigate atomic
Bose-Einstein condensates (BECs), with attraction between atoms, under the
action of strong transverse confinement and periodic (optical-lattice, OL)
axial potential. Using a combination of the variational approximation (VA),
one-dimensional (1D) nonpolynomial Schr\"{o}dinger equation (NPSE), and direct
numerical solutions of the underlying 3D Gross-Pitaevskii equation (GPE), we
show that the ground state of the condensate is a soliton belonging to the
semi-infinite bandgap of the periodic potential. The soliton may be confined to
a single cell of the lattice, or extend to several cells, depending on the
effective self-attraction strength, $g$ (which is proportional to the number of
atoms bound in the soliton), and depth of the potential, $V_{0}$, the increase
of $V_{0}$ leading to strong compression of the soliton. We demonstrate that
the OL is an effective tool to control the soliton's shape. It is found that,
due to the 3D character of the underlying setting, the ground-state soliton
collapses at a critical value of the strength, $g=g_{c}$, which gradually
decreases with the increase of the depth of the periodic potential, $V_{0}$;
under typical experimental conditions, the corresponding maximum number of
$^{7}$Li atoms in the soliton, $N_{\max}$, ranges between $8,000$ and $4,000$.
Examples of stable multi-peaked solitons are also found in the first finite
bandgap of the lattice spectrum. The respective critical value $g_{c}$ again
slowly decreases with the increase of $V_{0}$, corresponding to $N_{\max
}\simeq 5,000$.
