Pattern formation and clustering of solitons in nonlinear weakly-correlated wave-systems

Summary form only given. We have theoretically demonstrated that incoherent wave systems do exhibit modulation instability, but they do so only if the nonlinearity exceeds a threshold that is set by the degree of coherence. In other words, in such weakly-correlated multi-particle systems, uniform intensity inputs become unstable in a self-focusing environment if the nonlinearity exceeds a threshold set by the correlation distance (between the particles). In a recent series of experiments we have confirmed these predictions: that patterns can form spontaneously (from noise) in a nonlinear partially coherent system (a nonlinear system of weakly-correlated particles) when the nonlinearity exceeds the threshold, and a periodic train of one-dimensional filaments emerges. At a higher value of nonlinearity, we have discovered, unexpectedly, that the incoherent ID filaments break up into self-ordered arrays of light spots.