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Soliton turbulence as a thermodynamic limit of stochastic soliton lattices

Publication ,  Journal Article
El, GA; Krylov, AL; Molchanov, SA; Venakides, S
Published in: Physica D: Nonlinear Phenomena
May 15, 2001

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.

Duke Scholars

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

May 15, 2001

Volume

152-153

Start / End Page

653 / 664

Related Subject Headings

  • Fluids & Plasmas
  • 0102 Applied Mathematics
 

Citation

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El, G. A., Krylov, A. L., Molchanov, S. A., & Venakides, S. (2001). Soliton turbulence as a thermodynamic limit of stochastic soliton lattices. Physica D: Nonlinear Phenomena, 152153, 653–664. https://doi.org/10.1016/S0167-2789(01)00198-1
El, G. A., A. L. Krylov, S. A. Molchanov, and S. Venakides. “Soliton turbulence as a thermodynamic limit of stochastic soliton lattices.” Physica D: Nonlinear Phenomena 152–153 (May 15, 2001): 653–64. https://doi.org/10.1016/S0167-2789(01)00198-1.
El GA, Krylov AL, Molchanov SA, Venakides S. Soliton turbulence as a thermodynamic limit of stochastic soliton lattices. Physica D: Nonlinear Phenomena. 2001 May 15;152–153:653–64.
El, G. A., et al. “Soliton turbulence as a thermodynamic limit of stochastic soliton lattices.” Physica D: Nonlinear Phenomena, vol. 152–153, May 2001, pp. 653–64. Scopus, doi:10.1016/S0167-2789(01)00198-1.
El GA, Krylov AL, Molchanov SA, Venakides S. Soliton turbulence as a thermodynamic limit of stochastic soliton lattices. Physica D: Nonlinear Phenomena. 2001 May 15;152–153:653–664.
Journal cover image

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

May 15, 2001

Volume

152-153

Start / End Page

653 / 664

Related Subject Headings

  • Fluids & Plasmas
  • 0102 Applied Mathematics