Influence of noise on the formation of optical soiitons in waveguides

An analysis is made of the propagation of an electromagnetic pulse in a nonlinear fiber waveguide. A numerical solution of a nonlinear Schrödinger equation with an initial condition in the form of pulses subjected to random amplitude or phase modulation demonstrates that if a soliton is formed, then its position and propagation velocity experience fluctuations whereas the amplitude is affected very little. This should result in broadening of the average envelope of a pulse, but in each of the realizations of the random initial condition the resultant pulse may not experience broadening.