Spontaneously walking discrete cavity solitons

We study the dynamics of oscillating discrete solitons in an array of coupled Kerr-nonlinear cavities. They emanate from stationary discrete cavity solitons due to Hopf instability and are very robust. We show that these oscillating solitons can spontaneously lose their spatial symmetry and start rocking around the equilibrium position. Moreover they can suddenly jump to adjacent resonators starting a chaotic motion along the array, resembling the Brownian motion of particles. We also identify the parameter domain where they move with constant velocity across the array.