Samuil A. Rybak
N. N. Andreyev Acoustics Inst., 117036 Shvernik Str. 4, Moscow, Russia
Waves in media with fluctuating parameters are described with the help of a Green's function method. For the average field, the integral Dyson equation is formulated and its solution is obtained by means of the Bourret approximation. The average field (coherent part) decays exponentially with distance from the point source while the fluctuations grow. The Bethe--Salpeter equations are formulated for the average energy distribution. The ``ladder'' approximation then gives a system of transport integral equations which resemble heat transport equations. For the validity of the theory some threshold level of dissipation in the medium is necessary. The distribution of the fluctuations of the parameters is taken to be Gaussian. The solutions for energy distribution have an exponential decay with the index proportional to the root of the dissipation coefficient of the medium. In waveguides with fluctuating parameters the wave modes are coupled and both the coherent parts of these modes and the energy distributions are not independent. The energy fluxes become equal for traveling normal waves. Elastic plates with fluctuating parameters are examples of such waveguides for coupled longitudinal and flexural waves. Verification of the theory was made with the help of direct calculations for some simple models.