TY - JOUR
T1 - Soliton turbulence as a thermodynamic limit of stochastic soliton lattices
AU - El, Gennady A.
AU - Krylov, Alexander L.
AU - Molchanov, Stanislav A.
AU - Venakides, Stephanos
PY - 2001/5/15
Y1 - 2001/5/15
N2 - 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.
AB - 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.
KW - Finite-gap potentials
KW - Stochastic processes
KW - Thermodynamic limit
UR - http://www.scopus.com/inward/record.url?scp=4043063150&partnerID=8YFLogxK
U2 - 10.1016/S0167-2789(01)00198-1
DO - 10.1016/S0167-2789(01)00198-1
M3 - Article
AN - SCOPUS:4043063150
VL - 152-153
SP - 653
EP - 664
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
ER -