Stochastic instability of nonlinear waves and solitons of Korteweg - de Vries equation

This paper considers properties of nonlinear waves and solitons of Korteweg-de Vries equation in the presence of external perturbation. Basing on a method of stochastic destruction of separatrix, we obtain the criterion for stochasticity for such the waves. It shows that under any excitation nonlinear waves and solitons acquire the property of stirring and thereby become stochastically unstable. For particular form of perturbation we consider the fine structure of stochastic layer with regards to nonresonant terms. Obtained theoretical results find experimental confirmation in experiments with the propagation of ion-acoustic waves in plasma. PACS: 05.45.Y, 05.40, 52.35.S