Math @ Duke

Publications [#244156] of Stephanos Venakides
Papers Published
 El, GA; Krylov, AL; Molchanov, SA; Venakides, S, Soliton turbulence as a thermodynamic limit of stochastic soliton lattices,
Physica D: Nonlinear Phenomena, vol. 152153
(2001),
pp. 653664 [doi]
(last updated on 2018/03/23)
Abstract: 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 bandgap 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 onedimensional space with the random Poisson measure. The zerodensity limit of the soliton turbulence coincides with the FrishLloyd potential of the quantum theory of disordered systems. © 2001 Published by Elsevier Science B.V.


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