Langevin description of speckle dynamics in nonlinear disordered media

We formulate a Langevin description of dynamics of a speckle pattern resulting from the multiple scattering of a coherent wave in a nonlinear disordered medium. The speckle pattern exhibits instability with respect to periodic excitations at frequencies $\Omega$ below some ${\Omega }_{\max },$ provided that the nonlinearity exceeds some $\Omega$-dependent threshold. A transition of the speckle pattern from a stationary state to the chaotic evolution is predicted upon increasing nonlinearity. The shortest typical time scale of chaotic intensity fluctuations is of the order of $1/{\Omega }_{\max }.$