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 av eraged solution amplitudes exhibit in all cases algebraic decay, verif ying Wadati's universality conjecture. If the noise is time dependent, or position and time dependent, algebraic decay is obtained for inter mediate times too. These intermediate-time results agree well with the outcome of an experiment on ion-acoustic soliton propagation in a noi sy plasma. The distribution of soliton first passage times in a noisy medium is also discussed. [S1063-651X(98)10509-3].