Travelling Waves in a Chain of Coupled Nonlinear Oscillators

Abstract : In a chain of nonlinear oscillators, linearly coupled to their nearest neighbors, all travelling waves of small amplitude are found as solutions of finite dimensional reversible dynamical systems. The coupling constant and the inverse wave speed form the parameter space. The groundstate consists of a one-parameter family of periodic waves. It is realized in a certain parameter region containing all cases of light coupling. Beyond the border of this region the complexity of wave-forms increases via a succession of bifurcations. In this paper we give an appropriate formulation of this problem, prove the basic facts about the reduction to finite dimensions, show the existence of the ground states and discuss the first bifurcation by determining a normal form for the reduced system. Finally we show the existence of nanopterons, which are localized waves with a noncancelling periodic tail at infinity whose amplitude is exponentially small in the bifurcation parameter.
Complete list of metadatas

Cited literature [20 references]  Display  Hide  Download

https://hal.univ-cotedazur.fr/hal-01271086
Contributor : Gerard Iooss <>
Submitted on : Tuesday, February 9, 2016 - 8:34:12 AM
Last modification on : Thursday, April 4, 2019 - 10:18:05 AM
Long-term archiving on : Saturday, November 12, 2016 - 2:26:25 PM

File

Ioki07011.pdf
Files produced by the author(s)

Identifiers

Citation

Gérard Iooss, Klaus Kirchgässner. Travelling Waves in a Chain of Coupled Nonlinear Oscillators. Communications in Mathematical Physics, Springer Verlag, 2000, 211 (2), pp.26. ⟨10.1007/s002200050821⟩. ⟨hal-01271086⟩

Share

Metrics

Record views

454

Files downloads

155