Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices

Details Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices

2000-05-31

arxiv.org/abs/nlin/0005068v1

Phys. Rev. Lett. 85, 550 (2000)

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, 6 figures, to appear in Phys. Rev. Lett

Scientific paper

10.1103/PhysRevLett.85.550

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.

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