Dynamics of solitons under random perturbations

The dynamics of solitons is investigated in media with randomly inhomogeneous and fluctuating parameters. Some exact results of the theory of nonlinear stochastic waves are given. An analysis is made of various approximate approaches, e.g. of the mean field method and the Born approximation. Special attention is paid to the perturbation technique based on the inverse scattering transform and to the construction of the most adequate stochastic perturbation theory for solitons. The described formalism is used to investigate the evolution of nonlinear wave (soliton) parameters, and the statistical characteristics of radiation generated by solitons in fluctuating media are analysed also. The same approach makes it possible to take into account the simultaneous effect of random and regular (e.g., friction) perturbations on the dynamics of solitons. Examples are given of situations arising when one describes nonlinear waves in real physical systems.