On waves in random media in the diffusion-approximation regime

Abstract

The aim of this contribution is to present recent results obtained at the “Centre de Mathematiques Appliquees de 1’ Ecole Polytechnique” by the group working on waves in random media (F. Bailly, J. Chilian, J.F. Clouet, J.P. Fouque and J. Gamier). These results are based on various generalizations of classical diffusion-approximation results. In the first section we study the spreading of fin acoustic pulse travelling through a randomly layered medium (Clouet-Fouque [8] and Chilian [6]). In the second section we present a justification of the parabolic and white noise approximation for waves in random media in the high frequency regime leading to a stochastic Schrodinger equation (Bailly-Clouet-Fouque [3] and Bailly [2]). The third section is devoted to the effect of a weak nonlinearity on a wave equation with a random potential (Gamier [12]). In the last section we study the amplification of an incoherent optical pulse propagating in a nonlinear Kerr medium [10].