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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
; | | Date: |
19 Jul 2000 | | Subject: | Exactly Solvable and Integrable Systems; Chaotic Dynamics | nlin.SI nlin.CD | | 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 $N o infty$ (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. | | Source: | arXiv, nlin.SI/0007025 | | Services: | Forum | Review | PDF | Favorites | |
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