Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices

Preprint

31 May 2000

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.nlin/0005068

Abstract

In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of analyticity versus wave amplitude is observed. As a consequence of the discreteness, oscillatory linear instabilities, persisting for arbitrarily small amplitude in infinite lattices, appear for all wave numbers Q not equal to zero or \pi. Incommensurate analytic SWs with |Q|>\pi/2 may however appear as 'quasi-stable', as their instability growth rate is of higher order.

Keywords

OSCILLATORY INSTABILITIES
DIMENSIONAL NONLINEAR
NONLINEAR LATTICES
INCOMMENSURATE
STANDING WAVES
INSTABILITY
WAVE
SWS

All Related Versions

Version 1, 2000-05-31, ArXiv
Published version: Physical Review Letters, 85 (3), 550.

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