From Newton's cradle to the discrete p-Schr\"odinger equation
Dynamical Systems
2013-12-18 v1 Analysis of PDEs
Abstract
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-Schr\"odinger 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.
Keywords
Cite
@article{arxiv.1306.2105,
title = {From Newton's cradle to the discrete p-Schr\"odinger equation},
author = {Brigitte Bidégaray-Fesquet and Eric Dumas and Guillaume James},
journal= {arXiv preprint arXiv:1306.2105},
year = {2013}
}