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Related Experiment Videos

Two-dimensional discrete breathers: construction, stability, and bifurcations

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
|October 25, 2000
PubMed
Summary

Researchers developed a method to construct 2D discrete breathers. They identified three breather types on a square lattice, with distinct stabilities and locations, and analyzed their bifurcations into phonon modes.

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Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Mathematical physics

Background:

  • Discrete nonlinear Schrödinger equation models various physical systems.
  • Discrete breathers are localized energy modes in nonlinear lattices.
  • Understanding breather dynamics is crucial for nonlinear science.

Purpose of the Study:

  • To develop a general methodology for constructing 2D discrete breather excitations.
  • To investigate the types and stability of breathers in the discrete nonlinear Schrödinger equation on a square lattice.
  • To analyze the transition from localized breather modes to extended phonon modes.

Main Methods:

  • A novel construction methodology for 2D discrete breathers.
  • Application to the discrete nonlinear Schrödinger equation on a square lattice.

Related Experiment Videos

  • Frequency-power phase diagram analysis and continuation methods.

    • Main Results:

    • Identification of three distinct types of 2D discrete breathers.
    • Classification of breather stability based on their centering (plaquette, vertex, edge).
    • Observation of a triple point where breather branches bifurcate into extended phonon modes.

    Conclusions:

    • The developed methodology successfully constructs 2D discrete breathers.
    • Breather properties are highly dependent on their spatial localization.
    • The study elucidates the transition mechanism from localized to extended modes in nonlinear lattices.