Mesoscopic sensitivity of speckles in disordered nonlinear media to changes of disordered 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 enough sample size this quantity diverges, which implies that at given coherent wave incident on a sample there are multiple solutions for the spatial distribution of the wave's density. The number of solutions increases exponentially with the sample size.