Amplification of Nonlinear Waves in the Medium with Temporal Fluctuations

Abstract

The nonlinear wave propagation in random media seems to be very important physical phenomenon having a long and rich history. The scope of this paper is to highlight the main ideas of the new approach to this problem and to give an up-to-date view of the theory. The paper is organized in the following way. We start with the description and discussion of the so-called “mean field method” /1–3/. Then in Section 2 an exactly solvable model describing nonlinear wave propagation in the medium with fluctuating parameters /4/ is considered in order to demonstrate that the “mean field method” is correct. In Section 3 a specific asymptotic procedure of obtaining the equations for a mean wave form /5/ is presented. As an example, in Section 4 the description of the effect of nonlinear wave amplification in the medium with temporal fluctuations is given. In this case the amplification takes the form of an explosive instability.