Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices
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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