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Self-organization in nonlinear wave turbulence

Jordan1, Josserand

  • 1Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, Massachusetts 01609-2280, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 25, 2000
PubMed
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A new statistical model explains how nonlinear Schrodinger (NLS) equations self-organize. The system forms a stable solitary wave with random fluctuations, matching simulation results.

Area of Science:

  • Nonlinear dynamics
  • Statistical physics
  • Quantum mechanics

Background:

  • Nonlinear Schrodinger (NLS) equations describe various physical phenomena.
  • Understanding self-organization in these systems is crucial.
  • Previous models lacked a complete statistical description.

Purpose of the Study:

  • To develop a statistical equilibrium model for self-organization in focusing, nonintegrable NLS equations.
  • To predict the asymptotic-time behavior of NLS systems.
  • To validate the model against numerical simulations.

Main Methods:

  • Development of a statistical equilibrium model.
  • Analysis of Hamiltonian minimization under conserved particle number.
  • Direct numerical simulations of NLS equations.

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Main Results:

  • The model predicts the formation of a persistent large-scale coherent solitary wave.
  • Small-scale random fluctuations (radiation) account for energy differences.
  • Excellent qualitative and quantitative agreement between model predictions and numerical simulations.
  • Observation of transitory dynamics and scale-dependent statistical equilibrium.

Conclusions:

  • The statistical equilibrium model accurately describes NLS self-organization.
  • The system evolves towards a state minimizing Hamiltonian with conserved particle number.
  • Transitory dynamics reveal a progression towards statistical equilibrium across investigated scales.