We investigate spatial solitons in a resonator with a narrow-band gain
element and a saturable absorber placed in Fourier-conjugated resonat
or planes. Solitons are stationary or move at discrete velocities depe
nding on the resonator tuning. The modulus of the velocity of moving s
olitons is fixed, but the direction of their motion is arbitrary. Soli
tons compete in velocity space. The experiments are conducted on a pho
torefractive oscillator with bacteriorhodopsin saturable absorber. Obs
ervations agree well with solutions of a general order parameter equat
ion for such resonators. [S1050-2947(98)02701-2].