ABSTRACT
This chapter characterizes the most essential problems and models of stochastic wave analysis along with some new results concerning nonlinear stochastic wave propagation. The stochastic nature of real wave processes results above all from the inhomogeneity and complexity of the structure of most wave-transmitting media. Radio signals, laser beams, and light from stars transmitted through the atmosphere fluctuate in space and time. Independently of the differences associated with the specific physical problem, wave propagation in a stochastic medium is always connected with the phenomenon of scattering. Attenuation of wave is a decrease of wave amplitude due to scattering. Since wave intensity and energy are characterized by the amplitude, an attenuation means also the energy decay. Unlike linear, or small amplitude, waves that propagate without change of their profile, the nonlinear waves — represented by nonlinear partial differential equations — have many specific and characteristic features.
