Simulation of soliton formation in a uniform chain

Evolution of an arbitrary initial distribution of a quantum-mechanical particle in a uniform molecular chain is simulated by a system of coupled quantum-classical dynamical equations with dissipation. Stationary solutions of the system are determined by a nonlinear Schroedinger equation. An asymptotical expression is obtained for the time in which the soliton state is formed. The validity of the expression is checked by straightforward computational experiments. It is shown that the time of soliton formation depends strongly on the initial phase of the particle's wave function.