Soliton gas description of modulational instability
Thibaut Congy (Northumbria)
Soliton gases are infinite random ensembles of interacting solitons whose large-scale dynamics are governed by the elementary two-soliton collisions. By applying the spectral theory of soliton gases to the focusing nonlinear Schrödinger equation (fNLSE), we can describe the statistically stationary and spatially homogeneous integrable turbulence that emerges at large times from the spontaneous (noise-induced) modulational instability of the plane-wave and the elliptic "dn" solutions.
I will show that a special, critically dense soliton gas—the bound-state soliton condensate—provides an accurate model for the asymptotic state of both plane-wave and elliptic integrable turbulence. Moreover, certain statistical moments of the resulting turbulence can be computed analytically, allowing us to assess deviations from Gaussianity. These analytical predictions demonstrate excellent agreement with direct numerical simulations of the fNLSE.
The talk is based on the recent works:
- "Statistics of Extreme Events in Integrable Turbulence", T. Congy, G. A. El, G. Roberti, A. Tovbis, S. Randoux, and P. Suret, Phys. Rev. Lett. 132, 207201 (2024).
- "Spontaneous modulational instability of elliptic periodic waves: The soliton condensate model", D. S. Agafontsev, T. Congy, G. A. El, S. Randoux, G. Roberti, and P. Suret, Physica D 134956 (2025).
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