Breathers and surface modes in oscillator chains with Hertzian interactions

Guillaume James (1, 2) , Jesus Cuevas (3) , Panayotis G. Kevrekidis (4)

1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
2 CASYS - Calculs Algébriques et Systèmes Dynamiques
3 GFNL - Grupo de Física No Lineal
4 Department of Mathematics and Statistics [University of Massachusetts]

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.

Domaines: Formation de Structures et Solitons [nlin.PS]; Systèmes dynamiques [math.DS]

Guillaume James, Jesus Cuevas, Panayotis G. Kevrekidis. Breathers and surface modes in oscillator chains with Hertzian interactions. NOLTA 2012 - 2012 International Symposium on Nonlinear Theory and its Applications, Oct 2012, Palma de Majorca, Spain. pp.470-473. ⟨hal-00771479⟩