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arXiv · 1306.2105

From Newton's cradle to the discrete p-Schr\"odinger equation

Brigitte Bidégaray-Fesquet·Eric Dumas·Guillaume James
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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.

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Brigitte Bidégaray-Fesquet, Eric Dumas, Guillaume James. 2013-06-10. From Newton's cradle to the discrete p-Schr\"odinger equation. https://arxiv.org/abs/1306.2105

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