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2011, Volume 2011: 485-494. Doi: 10.3934/proc.2011.2011.485 open access
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Transport and generation of macroscopically modulated waves in diatomic chains

  • 1.

    Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, D-10117 Berlin

Received:  July 31, 2010
Revised:  March 31, 2011
Published:  August 2017
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    Abstract
  • We derive and justify analytically the dynamics of a small macroscopically modulated amplitude of a single plane wave in a nonlinear diatomic chain with stabilizing on-site potentials including the case where a wave generates another wave via self-interaction. More precisely, we show that in typical chains acoustical waves can generate optical but not acoustical waves, while optical waves are always closed with respect to self-interaction.
    Mathematics Subject Classification: Primary: 37K60, 34E13; Secondary: 70F45, 35L45.

    Citation:
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