A Statistical Model for Soliton Particle Interaction in Plasmas

A statistical model for soliton-particle interaction is presented. A master equation is derived for the time evolution of the particle velocity distribution as induced by resonant interaction with Korteweg-de Vries solitons. The detailed energy balance during the interaction subsequently determines the evolution of the soliton amplitude distribution. The analysis applies equally well for weakly nonlinear plasma waves in a strongly magnetized waveguide, or for ion acoustic waves propagating in one-dimensional systems.