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Soliton Turbulence as a Thermodynamic Limit of Stochastic Soliton Lattices

Gennady A. El·Alexander L. Krylov·Stanislav A. Molchanov·Stephanos Venakides
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Abstract

We use recently introduced notion of stochastic soliton lattice for quantitative description of soliton turbulence. We consider the stochastic soliton lattice on a special band-gap scaling of the spectral surface of genus $N$ so that the integrated density of states remains finite as $N \to \infty$ (thermodynamic type limit). We prove existence of the limiting stationary ergodic process and associate it with the soliton turbulence. The phase space of the soliton turbulence is a one-dimensional space with the random Poisson measure. The zero density limit of the soliton turbulence coincides with the Frish - Lloyd potential of the quantum theory of disordered systems.

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Gennady A. El, Alexander L. Krylov, Stanislav A. Molchanov, Stephanos Venakides. 2000-07-19. Soliton Turbulence as a Thermodynamic Limit of Stochastic Soliton Lattices. https://doi.org/10.1016/s0167-2789(01)00198-1

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