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Nonintegrable Schrodinger discrete breathers.

J Gómez-Gardeñes1, L M Floría, M Peyrard

  • 1Departamento de Teoría y Simulación de Sistemas Complejos, Instituto de Ciencia de Materiales de Aragón, C.S.I.C.-Universidad de Zaragoza, 50009 Zaragoza, Spain. gardenes@unizar.es

Chaos (Woodbury, N.Y.)
|December 1, 2004
PubMed
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Discrete breathers in nonlinear Schrödinger lattices exhibit translational motion, driven by a localized core interacting with an extended background wave. Numerical simulations reveal this complex interplay is crucial for energy balance and motion dynamics.

Area of Science:

  • Nonlinear physics
  • Condensed matter theory
  • Computational physics

Background:

  • Discrete breathers are localized nonlinear excitations in lattices.
  • Their translational motion in nonintegrable systems is complex.
  • Understanding their dynamics is key to nonlinear science.

Purpose of the Study:

  • To numerically investigate the translational motion of discrete breathers.
  • To analyze solutions originating from the integrable Ablowitz-Ladik lattice limit.
  • To understand the role of the background state in breather dynamics.

Main Methods:

  • Extensive numerical simulations.
  • Regularized Newton algorithm for solution continuation.
  • Analysis of breather structure as a superposition of core and background.

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Main Results:

  • Solutions consist of a localized moving core and an excited extended background.
  • The background is composed of nonlinear resonant plane waves.
  • The background is essential for the energy balance governing core motion.

Conclusions:

  • The translational motion of discrete breathers is governed by the interaction between a localized core and a background wave.
  • Numerical findings provide insights into the energy transfer mechanisms.
  • Perturbative theories are evaluated against detailed numerical evidence.