Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2001-04-09
Physica D 162 (2002) 53-94
Nonlinear Sciences
Pattern Formation and Solitons
57 pages, 21 figures, to be published in Physica D. Revised version: Figs. 5 and 12 (f) replaced, some new results added to Se
Scientific paper
10.1016/S0167-2789(01)00378-5
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 Schroedinger (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 nontrivial 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 pi/2, respectively. In one regime persisting breathers are found, while in the other regime the system rapidly thermalizes.
Aubry Serge
Johansson Magnus
Kopidakis Georgios
Morgante Anna Maria
No associations
LandOfFree
Standing wave instabilities in a chain of nonlinear coupled oscillators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Standing wave instabilities in a chain of nonlinear coupled oscillators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Standing wave instabilities in a chain of nonlinear coupled oscillators will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-626543