An asymptotic model for small amplitude solutions to Newton's cradle

Brigitte Bidégaray-Fesquet (1) , Eric Dumas (2) , Guillaume James (3, 4)

1 EDP - Equations aux Dérivées Partielles
2 IF - Institut Fourier
3 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
4 CASYS - Calculs Algébriques et Systèmes Dynamiques

We study the dynamics of a one-dimensional lattice of nonlinearly coupled oscillators. The class of problems addressed include Newton's cradle with Hertzian contact interactions. The Cauchy problem is studied yielding lower bounds for the existence time. We then derive an asymptotic model for small amplitude solutions over large times. This allows to prove the existence of breather-like solutions to the initial model. We also estimate the maximal dispersion of localized initial data.

Domaines: Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]; Physique mathématique [math-ph]

Brigitte Bidégaray-Fesquet, Eric Dumas, Guillaume James. An asymptotic model for small amplitude solutions to Newton's cradle. 2014 SIAM Conference on Nonlinear Waves and Coherent Structures, Aug 2014, Cambridge, United Kingdom. ⟨hal-00974845⟩