Soliton collective excitations in stochastic molecular crystals

The dynamics of soliton-type collective excitations in inhomogeneous molecular crystals is investigated. An average-field equation is derived for the statistically perturbed nonlinear Schrödinger equation. The changes in the soliton amplitude and velocity are found. The conditions under which the average-field method applies to stochastic nonlinear wave equations are studied for the example of a model equation.