Standing wave instabilities in a chain of nonlinear coupled oscillators
2002 (English)In: Physica D: Non-linear phenomena, ISSN 0167-2789, Vol. 162, no 1-2, 53-94 p.Article in journal (Refereed) Published
We consider existence and stability properties of nonlinear spatially periodic or quasiperiodic standing waves (SWs) in one-dimensional lattices of coupled anharmonic oscillators. Specifically, we consider Klein-Gordon (KG) chains with either soft (e.g., Morse) or hard (e.g., quartic) on-site potentials, as well as discrete nonlinear Schrödinger (DNLS) chains approximating the small-amplitude dynamics of KG chains with weak inter-site coupling. The SWs are constructed as exact time-periodic multibreather solutions from the anticontinuous limit of uncoupled oscillators. In the validity regime of the DNLS approximation these solutions can be continued into the linear phonon band, where they merge into standard harmonic SWs. For SWs with incommensurate wave vectors, this continuation is associated with an inverse transition by breaking of analyticity. When the DNLS approximation is not valid, the continuation may be interrupted by bifurcations associated with resonances with higher harmonics of the SW. Concerning the stability, we identify one class of SWs which are always linearly stable close to the anticontinuous limit. However, approaching the linear limit all SWs with non-trivial wave vectors become unstable through oscillatory instabilities, persisting for arbitrarily small amplitudes in infinite lattices. Investigating the dynamics resulting from these instabilities, we find two qualitatively different regimes for wave vectors smaller than or larger than p/2, respectively. In one regime persisting breathers are found, while in the other regime the system rapidly thermalizes. © 2002 Elsevier Science B.V. All rights reserved.
Place, publisher, year, edition, pages
2002. Vol. 162, no 1-2, 53-94 p.
Anharmonic lattices, Breaking of analyticity, Nonlinear standing waves, Oscillatory instabilities
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-46979DOI: 10.1016/S0167-2789(01)00378-5OAI: oai:DiVA.org:liu-46979DiVA: diva2:267875