Soliton turbulence as a thermodynamic limit of stochastic soliton lattices

Journal Article (Journal Article)

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. © 2001 Published by Elsevier Science B.V.

Full Text

Duke Authors

Cited Authors

  • El, GA; Krylov, AL; Molchanov, SA; Venakides, S

Published Date

  • May 15, 2001

Published In

Volume / Issue

  • 152-153 /

Start / End Page

  • 653 - 664

International Standard Serial Number (ISSN)

  • 0167-2789

Digital Object Identifier (DOI)

  • 10.1016/S0167-2789(01)00198-1

Citation Source

  • Scopus