Soliton turbulence as a thermodynamic limit of stochastic soliton lattices

We use the recently introduced notion of stochastic soliton lattice for qua ntitative description of soliton turbulence. We consider the stochastic sol iton lattice on a special band-gap scaling of the spectral surface of genus N so that the integrated density of states remains finite as N --> infinit y (thermodynamic type limit). We prove existence of the limiting stationary ergodic process and associate it with the homogeneous soliton turbulence. The phase space of the soliton turbulence is a one-dimensional space with t he random Poisson measure. The zero-density limit of the soliton turbulence coincides with the Frish-Lloyd potential of the quantum theory of disorder ed systems. (C) 2001 Published by Elsevier Science B.V.