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Persistent breathers in long-ranged discrete nonlinear Schrödinger models.

C Brunhuber1, F G Mertens, Y Gaididei

  • 1Physikalisches Institut, Universität Bayreuth, Germany. Christian.Brunhuber@uni-bayreuth.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 29, 2006
PubMed
Summary

The discrete nonlinear Schrödinger (DNLS) model with long-range interactions and damping creates periodic patterns of stationary breathers. These patterns arise from uniform backgrounds and depend on interaction range and system energy.

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Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Computational physics

Background:

  • The discrete nonlinear Schrödinger (DNLS) model is crucial for studying wave phenomena.
  • Long-range interactions and nonlinear damping significantly influence system behavior.
  • Stationary breathers are localized energy packets that can persist in nonlinear systems.

Purpose of the Study:

  • To investigate the effects of Kac-Baker long-range interactions and nonlinear damping in the DNLS model.
  • To analyze the formation of periodic patterns of stationary breathers.
  • To understand the transition to the persistent-breather phase in undamped systems.

Main Methods:

  • Computer simulations were employed to observe system dynamics.
  • The quasicontinuum approximation was used to analyze periodicity.

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  • Monte Carlo techniques were utilized to study localization strength.

    • Main Results:

    • The combination of long-range forces and damping generates periodic stationary breathers from uniform backgrounds.
    • The inverse interaction radius dictates the observed periodicity.
    • In undamped systems, long-range interactions influence the transition to the persistent-breather phase, dependent on energy and norm.

    Conclusions:

    • The DNLS model with specific interactions and damping exhibits predictable breather formation.
    • System parameters like interaction radius and energy control breather dynamics and phase transitions.
    • Localization strength can be monitored as a function of interaction range and temperature.