Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices

Anna Maria Morgante, Magnus Johansson, Georgios Kopidakis, and Serge Aubry
Phys. Rev. Lett. 85, 550 – Published 17 July 2000
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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 Q0, π. Incommensurate analytic SWs with |Q|>π/2 may however appear as “quasistable,” as their instability growth rate is of higher order.

  • Received 2 February 2000

DOI:https://doi.org/10.1103/PhysRevLett.85.550

©2000 American Physical Society

Authors & Affiliations

Anna Maria Morgante, Magnus Johansson, Georgios Kopidakis, and Serge Aubry

  • Laboratoire Léon Brillouin (CEA-CNRS), CEA Saclay, F-91191 Gif-sur-Yvette Cedex, France

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Issue

Vol. 85, Iss. 3 — 17 July 2000

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