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 , . Incommensurate analytic SWs with 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