Exactly Solvable Model of Wave-Mean Field Interaction in Integrable Turbulence

T. Congy; G. A. El; M. A. Hoefer

doi:10.1103/d2br-hl5x

Exactly Solvable Model of Wave-Mean Field Interaction in Integrable Turbulence

T. Congy^*, G. A. El, M. A. Hoefer

^*Corresponding author for this work

School of Engineering Physics and Mathematics

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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 an induced mean field and SG filtering. 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.

Original language	English
Article number	147201
Number of pages	8
Journal	Physical Review Letters
Volume	136
Issue number	14
Early online date	6 Apr 2026
DOIs	https://doi.org/10.1103/d2br-hl5x
Publication status	Published - 10 Apr 2026

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title = "Exactly Solvable Model of Wave-Mean Field Interaction in Integrable Turbulence",

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 an induced mean field and SG filtering. 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.",

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AU - El, G. A.

AU - Hoefer, M. A.

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Y1 - 2026/4/10

N2 - 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 an induced mean field and SG filtering. 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.

AB - 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 an induced mean field and SG filtering. 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.

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DO - 10.1103/d2br-hl5x

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JO - Physical Review Letters

JF - Physical Review Letters

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Exactly Solvable Model of Wave-Mean Field Interaction in Integrable Turbulence

Abstract

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