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Compactlike breathers: bridging the continuous with the anticontinuous limit

Eleftheriou1, Dey, Tsironis

  • 1Department of Physics, University of Crete and Foundation for Research and Technology-Hellas, P. O. Box 2208, 71003 Heraklion, Crete, Greece.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|December 2, 2000
PubMed
Summary

Discrete nonlinear lattices exhibit compacton solutions that maintain their compact support from the continuous to the anticontinuous limit. These stable discrete compact breathers retain their shape, even near the anticontinuous limit.

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Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Mathematical physics

Background:

  • Discrete nonlinear lattices exhibit complex behaviors.
  • Compacton solutions are known in continuous models.
  • Understanding discrete analogs is crucial for physical systems.

Purpose of the Study:

  • Investigate the persistence of compacton solutions in discrete nonlinear lattices.
  • Analyze the behavior of discrete compact breathers in the anticontinuous limit.
  • Determine the stability of these discrete compact breather solutions.

Main Methods:

  • Theoretical analysis of discrete nonlinear lattices.
  • Numerical exact procedures for generating solutions.
  • Analysis of solution shapes in different coupling regimes.

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Main Results:

  • Compact support of solutions persists from continuous to anticontinuous limits.
  • Discrete compact breathers retain a cosinelike shape in the large coupling regime.
  • Near the anticontinuous limit, solutions exhibit stretched exponential decay, preserving compactness.
  • Generated discrete compact breathers are generally stable.

Conclusions:

  • Compacton properties are robust in discrete nonlinear lattices.
  • Discrete compact breathers offer stable localized solutions.
  • The study provides insights into nonlinear wave phenomena in discrete systems.