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

Mini-Symposium on Nonlinear Dynamics of Granular CrystalsInternational audienceWe 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