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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
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
Abstract : 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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  • HAL Id : hal-00771479, version 1
  • ARXIV : 1301.1769

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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⟩

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