Perturbations propagation in self-organized patterns

In optical cavities, self-organized patterns can emerge because of diffraction and optical nonlinearities. This phenomena can be used to induce self-organization of an atomic cloud. Thus, this pattern can be understood as a lattice of cold atomic groups coupled by diffraction. From this point of view, there is an analogy between this system and a lattice
of atoms in a solid. From solid-state theory, a perturbation of the position of an atom in the lattice leads to a sound wave that propagates along the solid. Following this idea, our aim in this work is to study the response of a self-organized
pattern to a localized perturbation at one of the pattern peaks. Since the system is highly dissipative, we first study the dynamics of this system in order to choose a set of parameters close to a critical point in such a way that gain can counterbalance dissipation allowing the perturbations to propagate longer . Next, we run numerical simulations of our differential equation, taking as an initial condition the perturbed pattern. From the numerical results we extract propagation features such as the velocity, period, symmetry, etc. Finally, we characterize the perturbation propagation theoretically, and compare the analytical results with the numerical integration.