American Institute of Mathematical Sciences

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2011, 2011(Special): 485-494. doi: 10.3934/proc.2011.2011.485

Transport and generation of macroscopically modulated waves in diatomic chains

Johannes Giannoulis 1,

1. 

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

Received  August 2010 Revised  April 2011 Published  October 2011

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.
Keywords: macroscopic modulations, resonance conditions, Diatomic chains.
Mathematics Subject Classification: Primary: 37K60, 34E13; Secondary: 70F45, 35L45.
Citation: Johannes Giannoulis. Transport and generation of macroscopically modulated waves in diatomic chains. Conference Publications, 2011, 2011 (Special) : 485-494. doi: 10.3934/proc.2011.2011.485
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