EQUILIBRIUM DISTRIBUTION FUNCTION FOR KDV AND MODIFIED KDV SOLITONS IN A FLUCTUATING ENVIRONNMENT

Starting from the Boussinesq equation (BqE) with dissipation and fluct uation terms, modelling several solid-state systems, we get the corres ponding Korteweg-de Vries (KdV) equation for the unidirectional waves. Then we derive the Fokker-Planck equation for the amplitude of the Kd V soliton, and we find its stationary solution. The solution represent s a normalizable distribution function, which up to a pre-exponential factor has the canonical Boltzmann form in terms of the underlying BqE . We have also solved the same problem for the modified Bq/KdV equatio n.