  We study families of solitons in a two-dimensional (2D) model of the light
transmission through a photorefractive medium equipped with a
(quasi-)one-dimensional photonic lattice. The soliton families are bounded from
below by finite minimum values of the peak and total power. Narrow solitons
have a single maximum, while broader ones feature side lobes. Stability of the
solitons is checked by direct simulations. The solitons can be set in motion
across the lattice (actually, made tilted in the spatial domain), provided that
the respective boost parameter does not exceed a critical value. Collisions
between moving solitons are studied too. Collisions destroy the solitons,
unless their velocities are sufficiently small. In the latter case, the
colliding solitons merge into a single stable pulse.
