We show that in a cavity soliton laser based on a VCSEL with a saturable absorber the solitons can spontaneously move if the ratio of the carrier lifetimes in the amplifier and in the absorber takes appropriate values. The velocity is determined by the parameters of the system. In devices with a finite circular cross section the solitons move on circular trajectories along the boundary. This dynamical regime can be exploited to create trains of pulses with controlled intensity, frequency and wherein a determined delay can be applied.
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