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Discrete nonlinear Schrödinger equation with defects.

A Trombettoni1, A Smerzi, A R Bishop

  • 1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 15, 2003
PubMed
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We studied wave dynamics in a disordered nonlinear system, revealing distinct behaviors like complete reflection, stable oscillations, and self-trapping. These findings offer insights into wave propagation through imperfect nonlinear media.

Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Wave propagation

Background:

  • The discrete nonlinear Schrödinger equation (DNLS) models wave phenomena in various physical systems.
  • Understanding wave dynamics in disordered systems is crucial for many applications.
  • On-site defects introduce complexity to wave propagation.

Purpose of the Study:

  • To investigate the dynamical properties of the one-dimensional DNLS with defects.
  • To analyze the behavior of traveling plane waves under specific conditions.
  • To map the system's dynamics to a simplified Hamiltonian model.

Main Methods:

  • Analysis of the one-dimensional DNLS with periodic boundary conditions and on-site defects.
  • Study of traveling plane wave propagation using a two-mode ansatz in Fourier space.

Related Experiment Videos

  • Mapping system dynamics to a nonrigid pendulum Hamiltonian for analytical prediction and numerical confirmation.

    • Main Results:

    • Identified three distinct dynamical regimes: complete reflection/refocusing, quasi-stationary oscillations, and self-trapping.
    • Demonstrated that wave dynamics can be accurately described by a nonrigid pendulum Hamiltonian.
    • Confirmed analytical predictions through numerical simulations.

    Conclusions:

    • The two-mode ansatz effectively captures the essential dynamics of the DNLS with defects.
    • The system exhibits rich dynamical behaviors dependent on nonlinearity and defect distribution.
    • The study provides a framework for understanding wave propagation in complex nonlinear media.