Soliton Turbulence as a Thermodynamic Limit of Stochastic Soliton Lattices

Details Soliton Turbulence as a Thermodynamic Limit of Stochastic Soliton Lattices Soliton Turbulence as a Thermodynamic Limit of Stochastic Soliton Lattices

2000-07-19

arxiv.org/abs/nlin/0007025v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages, Latex. This is the report presented at the conference "Theoretical Physics, Solitons and Turbulence" in honour of th

Scientific paper

10.1016/S0167-2789(01)00198-1

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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