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We consider the multiple scattering of a scalar wave in a disordered mediumwith a weak nonlinearity of Kerr type. The perturbation theory, developed tocalculate the temporal autocorrelation function of scattered wave, fails atshort correlation times. A self-consistent calculation shows that fornonlinearities exceeding a certain threshold value, the multiple-scatteringspeckle pattern becomes unstable and exhibits spontaneous fluctuations even inthe absence of scatterer motion. The instability is due to a distributedfeedback in the system "coherent wave + nonlinear disordered medium". Thefeedback is provided by the multiple scattering. The development of instabilityis independent of the sign of nonlinearity.Comment: RevTeX, 15 pages (including 5 figures), accepted for publication in  Phys. Rev.

Temporal fluctuations of waves in weakly nonlinear disordered media