Random Waves in Nonlinear Dispersive Media

This text contains a survey of theories describing the evolution of random waves in nonlinear dispersive media. The three kinds of problems are considered, and the applications of theory to the problem of condensed matter physics and nonlinear optics are discussed for each type of problem.

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This text contains a survey of theories describing the evolution of random waves in nonlinear dispersive media. The three kinds of problems are considered. The first is the investigation of the evolution of initially random waves in nonlinear media describing the integrable and nearly integrable systems. It is important for many branches of acoustics and nonlinear optics, in particular for soliton transmissions in long optical communication systems. The second is the nonlinear waves propagation in the media with random parameters. The cases of stationary and nonstationary inhomogeneities are studied. The third is the investigation of chaotic behaviour of nonlinear waves under deterministic perturbations (dynamical chaos of nonlinear waves). The applications of theory to the problem of condensed matter physics and nonlinear optics are discussed for each type of problem.