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Localized excitations and their thresholds

Kevrekidis1, Rasmussen, Bishop

  • 1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 and Department of Physics and Astronomy, Rutgers University 136 Frelinghuysen Road, Piscataway, New Jersey 08854-8019, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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We developed a fast numerical method to find localized excitations in discrete nonlinear Schrödinger models. This technique efficiently identifies breather excitations in multiple dimensions with super-linear convergence.

Area of Science:

  • Computational Physics
  • Nonlinear Dynamics
  • Mathematical Modeling

Background:

  • Discrete nonlinear Schrödinger (DNLS) models are crucial for understanding wave phenomena.
  • Identifying localized excitations (e.g., breathers) is key to analyzing DNLS model behavior.
  • Existing methods for finding these excitations can be computationally intensive.

Purpose of the Study:

  • To introduce a novel, efficient numerical method for detecting localized excitations in DNLS models.
  • To demonstrate the method's capability in identifying breather solutions across various dimensions.
  • To validate the method's performance against established theoretical criteria.

Main Methods:

  • A nonlinear iterative approach based on the Rayleigh-Ritz variational principle was employed.

Related Experiment Videos

  • The method was applied to identify breather excitations in one and higher spatial dimensions.
  • Convergence properties of the numerical method were analyzed, revealing super-linear convergence.

    • Main Results:

    • The proposed numerical method rapidly and efficiently identifies breather excitations.
    • Super-linear convergence rates were observed for the iterative technique.
    • The method's utility was confirmed by studying excitation power thresholds for nonlinear modes.

    Conclusions:

    • The developed numerical method offers a fast and efficient tool for analyzing localized excitations in DNLS models.
    • This technique provides a valuable approach for exploring the dynamics and stability of nonlinear modes.
    • The findings facilitate further theoretical and computational investigations into complex nonlinear systems.