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Bright compact breathers.

P G Kevrekidis1, V V Konotop

  • 1Department of Mathematics and Statistics, University of Massachusetts, Lederle Graduate Research Tower, Amherst, MA 01003-4515, USA. kevrekid@math.umass.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 22, 2002
PubMed
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This study explores bright discrete compact breather solutions in nonlinear lattice models. Stable compact breather solutions were found in one-parameter families, while zero-parameter families yielded unstable solutions.

Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Mathematical physics

Background:

  • Nonlinear lattice models are crucial for understanding complex physical phenomena.
  • Discrete breathers are localized nonlinear excitations in such models.
  • Investigating compact breather solutions (compactlets) offers insights into energy localization.

Purpose of the Study:

  • To analyze the potential of general nonlinear lattice models to support bright discrete compact breather solutions.
  • To classify models based on the existence and parameterization of compact breather solutions.
  • To investigate the linear stability of these compact breather solutions.

Main Methods:

  • Classification of nonlinear lattice models into three categories based on compact breather solution existence.

Related Experiment Videos

  • Construction of compact breather solutions for models supporting them.
  • Linear stability analysis of the derived compact breather solutions.

    • Main Results:

    • Identified three classes of models: no compact breathers, one-parameter families of solutions, and 'isolated' solutions.
    • Constructed and analyzed the linear stability of solutions in the latter two classes.
    • Found stable compact breather solutions in one-parameter families, contrasting with unstable solutions in zero-parameter families.

    Conclusions:

    • Nonlinear lattice models exhibit diverse behaviors regarding compact breather solutions.
    • The stability of compact breathers significantly differs from smoothly decaying counterparts.
    • One-parameter families are key to finding stable bright discrete compact breather solutions.