| Contents |
| We investigate the dynamics of a chain of oscillators coupled by fully-
nonlinear interaction potentials. This class of models includes Newton's
cradle with Hertzian contact interactions between neighbors. By means
of multiple-scale analysis, we give a rigorous asymptotic description
of small amplitude solutions over large times. The envelope equation
leading to approximate solutions is a discrete p-Schroedinger equation.
Our results include the existence of long-lived breather solutions to
the original model. For a large class of localized initial conditions,
we also estimate the maximal decay of small amplitude solutions over
long times. |
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