Solitons and shock waves under random external noise
The paper treats nonlinear wave processes under random external noise. The two basic equations considered are the Korteweg-de Vries and Burgers equations, governing nonlinear wave processes with dispersion and dissipation, respectively. A basic feature of these equations is the existence of stable wave profiles, called solitons, and shock waves, respectively in the two cases. Under additive noise perturbation (depending only on time) it is shown that a suitable change of variable reduces the stochastic equation to a deterministic one of classical form. The stationary random solution (soliton or shock wave) obtained explicitly by this procedure is a function of the noise. Mean and variance of this random wave are in exact or approximated form, and graphically illustrated. Among the results of physical significance, it is shown that the noise causes damping of the solitons.
scientific article; zbMATH DE number 4201297