An exactly solvable model of wave-mean field interaction in integrable turbulence

The kinetic theory of soliton gases (SG) is used to develop a solvable model for wave-mean field interaction in integrable turbulence. The waves are stochastic soliton ensembles that scatter off a critically dense SG or soliton condensate -- the mean field. The derived two-fluid kinetic-hydrodynamic equations admit exact solutions predicting SG filtering and an induced mean field. The obtained SG statistical moments agree with ensemble averages of numerical simulations. The developed theory readily generalizes, with applications in fluids, nonlinear optics and condensed matter.