A statistical approach of the decay of a soliton in a randomly perturbed Toda chain

Abstract

This paper addresses the soliton dynamics in a Toda lattice with a randomly distributed chain of masses. Applying the inverse scattering transform we derive effective equations for the decay of the soliton amplitude that take into account radiative losses. The decay rate does not depend on the incoming energy for large amplitude soliton. An important feature is the generation of a soliton gas consisting of a large collection of small solitons. The soliton gas plays an important role in that the changes in the conservation equations cannot be correctly understood if the soliton production is neglected.