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Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices

Anna Maria Morgante·Magnus Johansson·Georgios Kopidakis·Serge Aubry
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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 Q not equal to zero or π. Incommensurate analytic SWs with |Q|>π/2 may however appear as 'quasi-stable', as their instability growth rate is of higher order.

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Anna Maria Morgante, Magnus Johansson, Georgios Kopidakis, Serge Aubry. 2000-05-31. Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices. https://doi.org/10.1103/physrevlett.85.550

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