Nonlinear Wave-packet Dynamics in a Disordered Medium
The propagation of a wave-packet in a nonlinear disordered medium exhibits interesting dynamics. This problem is directly connected to experiments on expanding Bose gases and to studies of transverse localization in nonlinear optical media.
In a nonlinear medium the energy of the wave-packet is stored both in the kinetic and potential parts, and details of its propagation are to a large extent determined by the transfer from one form of energy to the other. In this talk, I will describe an effective theory of pulse propagation in a nonlinear and disordered medium. Based on estimates for the scattering rate, I will then discuss the relevance of the nonlinearity for the localization problem.