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2011, Volume 2011: 485-494. Doi: 10.3934/proc.2011.2011.485 open access
This issue Previous Article Comparing the efficiency of numerical techniques for the integration of variational equations Next Article $L^1$ maximal regularity for the laplacian and applications

Transport and generation of macroscopically modulated waves in diatomic chains

  • 1.

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

Received:  August 2010
Revised:  April 2011
Published:  August 2017
Abstract / Introduction Related Papers Cited by
    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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