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

TL;DR

This paper develops an exactly solvable kinetic model for wave-mean field interactions in integrable turbulence, demonstrating soliton ensemble filtering and mean field effects with results validated by numerical simulations.

Contribution

It introduces a novel solvable kinetic-hydrodynamic model for soliton gases interacting with mean fields in integrable turbulence.

Findings

Exact solutions predict soliton gas filtering.

Statistical moments match numerical ensemble averages.

Model applicable to fluids, optics, and condensed matter.

Abstract

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.