BOUND-STATES IN A GAS OF SOLITONS SUPPORTED BY A RANDOMLY FLUCTUATINGFORCE

A non-linear Schrodinger equation with small terms accounting for diss ipation and a driving force randomly varying in time is considered. Ph ysical applications of this model are, e.g., Langmuir waves in a plasm a driven by a random electric field, or a randomly pumped non-linear o ptical fibre. The analysis is developed for the <<high-temperature>> c ase, when the drive is essentially stronger than the dissipation. In t his case, it is possible to introduce a mean potential of the soliton- soliton interaction, defined as the known usual potential (containing an oscillatory tail generated by the dissipative term) averaged over a n equilibrium distribution of the soliton's amplitude, which is produc ed by the corresponding Fokker-Planck equation. It is demonstrated tha t the mean potential contains a set of local minima, which should give rise to bound states in the rarefied gas of solitons supported by the random drive. An equilibrium separation between the solitons in the b ound states depends, in the <<high-temperature>> approximation, only o n the dissipative constant, but not on the <<temperature>> (mean-squar ed amplitude of the random drive).