Soliton turbulence as a thermodynamic limit of stochastic soliton lattices

Gennady A. El*, Alexander L. Krylov, Stanislav A. Molchanov, Stephanos Venakides

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


We use the 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 → ∞ (thermodynamic type limit). We prove existence of the limiting stationary ergodic process and associate it with the homogeneous 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.

Original languageEnglish
Pages (from-to)653-664
Number of pages12
JournalPhysica D: Nonlinear Phenomena
Early online date7 May 2001
Publication statusPublished - 15 May 2001
Externally publishedYes


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