Mesoscopic sensitivity of speckles in disordered nonlinear media to changes of the scattering potential

We show that the sensitivity of wave speckle patterns in disordered nonlinear media to changes of scattering potential increases with sample size. For large sizes the sensitivity diverges, which implies that for a given coherent wave incident on a sample there are multiple solutions for the spatial distribution of the wave density. The number of solutions increases exponentially with the sample size.