Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:B4L-A

Session:

Number:470

Breathers and surface modes in oscillator chains with Hertzian interactions

Guillaume James,  Jesús Cuevas,  Panayotis G. Kevrekidis,  

pp.470-473

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.470

PDF download (390KB)

Summary:
We study localized waves in chains of oscillators coupled by Hertzian interactions and trapped in local potentials. This problem is originally motivated by Newton's cradle, a mechanical system consisting of a chain of touching beads subject to gravity and attached to inelastic strings. We consider an unusual setting with local oscillations and collisions acting on similar time scales, a situation corresponding e.g. to a modified Newton's cradle with beads mounted on stiff cantilevers. Such systems support static and traveling breathers with unusual properties, including double exponential spatial decay, almost vanishing Peierls-Nabarro barrier and spontaneous direction-reversing motion. We prove analytically the existence of surface modes and static breathers for anharmonic on-site potentials and weak Hertzian interactions.

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