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We study families of solitons in a two-dimensional (2D) model of the lighttransmission through a photorefractive medium equipped with a(quasi-)one-dimensional photonic lattice. The soliton families are bounded frombelow by finite minimum values of the peak and total power. Narrow solitonshave a single maximum, while broader ones feature side lobes. Stability of thesolitons is checked by direct simulations. The solitons can be set in motionacross the lattice (actually, made tilted in the spatial domain), provided thatthe respective boost parameter does not exceed a critical value. Collisionsbetween moving solitons are studied too. Collisions destroy the solitons,unless their velocities are sufficiently small. In the latter case, thecolliding solitons merge into a single stable pulse.Comment: 14 pages, 9 figures, Physical Review E, in pres

Two-dimensional solitons in saturable media with a quasi-one-dimensional lattice potential