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Transport and generation of macroscopically modulated waves in diatomic chains

Pages: 485 - 494, Issue Special, September 2011

 Abstract        Full Text (336.6K)              

Johannes Giannoulis - Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, D-10117 Berlin, Germany (email)

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.

Keywords:  Diatomic chains, macroscopic modulations, resonance conditions
Mathematics Subject Classification:  Primary: 37K60, 34E13; Secondary: 70F45, 35L45

Received: August 2010;      Revised: April 2011;      Published: October 2011.