Spontaneous Motion of Cavity Solitons Induced by a Delayed Feedback

We study the properties of 2D cavity solitons in a coherently driven optical resonator subjected to a delayed feedback. The delay is found to induce a spontaneous motion of a single cavity soliton that is stationary and stable otherwise. This behavior occurs when the product of the delay time and the feedback strength exceeds some critical value. We derive an analytical formula for the speed of a moving soliton. Numerical results are in good agreement with analytical predictions.