Instabilities of waves in nonlinear disordered media

We develop a self-consistent theory of temporal fluctuations of a speckle p attern resulting from the multiple scattering of a coherent wave in a weakl y nonlinear disordered medium. The speckle pattern is shown to become unsta ble if the nonlinearity exceeds a threshold value. The instability is due t o a feedback provided by the multiple scattering and manifests itself in sp ontaneous fluctuations of the scattered intensity. The development of insta bility is independent of the sign of nonlinearity.