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Twisted localized modes.

P G Kevrekidis1, A R Bishop, K Ø Rasmussen

  • 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
|April 20, 2001
PubMed
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Researchers investigated twisted localized modes in the discrete nonlinear Schrödinger equation. They analyzed the stability and existence of these modes, identifying bifurcations and tracking their behavior even when unstable.

Area of Science:

  • Nonlinear dynamics
  • Mathematical physics
  • Quantum mechanics

Background:

  • Recent research proposed twisted localized modes for the discrete nonlinear Schrödinger equation.
  • Understanding the properties of these modes is crucial for nonlinear physics.

Purpose of the Study:

  • To investigate the existence and stability of twisted localized modes.
  • To analyze the persistence of quasiperiodic modes.
  • To identify bifurcations leading to instability.

Main Methods:

  • Analysis of existence domains.
  • Numerical stability analysis.
  • Bifurcation theory.
  • Tracking eigenmode behavior in unstable regimes.

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Main Results:

  • Established conditions for the existence of twisted localized modes.
  • Identified specific bifurcations causing mode instability.
  • Demonstrated the persistence of quasiperiodic modes.
  • Characterized the behavior of modes and their eigenmodes in unstable states.

Conclusions:

  • Twisted localized modes exhibit complex stability properties.
  • Bifurcations play a key role in the transition to instability.
  • Quasiperiodic modes can persist under certain conditions.
  • The study provides insights into nonlinear localized phenomena.