  We demonstrate that an important class of nonlinear stationary solutions of
the three-dimensional (3D) Gross-Pitaevskii equation (GPE) exhibiting
nontrivial transversal configurations can be found and characterized in terms
of an effective one-dimensional (1D) model. Using a variational approach we
derive effective equations of lower dimensionality for BECs in $(m,n_{r})$
transversal states (states featuring a central vortex of charge $m$ as well as
$n_{r}$ concentric zero-density rings at every $z$ plane) which provides us
with a good approximate solution of the original 3D problem. Since the
specifics of the transversal dynamics can be absorbed in the renormalization of
a couple of parameters, the functional form of the equations obtained is
universal. The model proposed finds its principal application in the study of
the existence and classification of 3D gap solitons supported by 1D optical
lattices, where in addition to providing a good estimate for the 3D wave
functions it is able to make very good predictions for the $\mu(N)$ curves
characterizing the different fundamental families. We have corroborated the
validity of our model by comparing its predictions with those from the exact
numerical solution of the full 3D GPE.
