Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices
Pattern Formation and Solitons
2009-10-31 v1 Condensed Matter
Chaotic Dynamics
Optics
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
Cite
@article{arxiv.nlin/0005068,
title = {Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices},
author = {Anna Maria Morgante and Magnus Johansson and Georgios Kopidakis and Serge Aubry},
journal= {arXiv preprint arXiv:nlin/0005068},
year = {2009}
}
Comments
4 pages, 6 figures, to appear in Phys. Rev. Lett