Abstract
In one-dimensional nonlinear lattices we construct nonlinear standing waves which for small amplitudes become harmonic, and we discuss their stability. If the spatial periodicity of the wave is incommensurate with the lattice period we observe a transition by breaking of analyticity for increasing wave amplitude. As a consequence of discreteness, standing waves in an infinite lattice are unstable through an oscillatory instability for all wave vectors 0 < Q < π for weak nonlinearity. For analytic incommensurate standing waves in a soft (hard) potential with, the |Q| > π/2(|Q| < π/2), instability shows up only at higher orders: these waves then appear as “quasi-stable”.
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Morgante, A.M., Johansson, M., Kopidakis, G., Aubry, S. (2001). Standing Waves in 1D Nonlinear Lattices. In: Abdullaev, F., Bang, O., Sørensen, M.P. (eds) Nonlinearity and Disorder: Theory and Applications. NATO Science Series, vol 45. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0542-5_16
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DOI: https://doi.org/10.1007/978-94-010-0542-5_16
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