Korteweg-de Vries solitons under additive stochastic perturbations

The evolution of solitonic solutions of the Korteweg-de Vries equation subject to additive noise is investigated using numerical techniques. Various types of additive white Gaussian noise are considered. The averaged solution amplitudes exhibit in all cases algebraic decay, verifying Wadati's universality conjecture. If the noise is time dependent, or position and time dependent, algebraic decay is obtained for intermediate times too. These intermediate-time results agree well with the outcome of an experiment on ion-acoustic soliton propagation in a noisy plasma. The distribution of soliton first passage times in a noisy medium is also discussed. [S1063-651X(98)10509-3].