Bidégaray-Fesquet, Brigitte; Dumas, Eric; James, Guillaume From Newton’s cradle to the discrete \(p\)-Schrödinger equation. (English) Zbl 1292.34008 SIAM J. Math. Anal. 45, No. 6, 3404-3430 (2013). Authors’ 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 \(p\)-Schrödinger 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. Reviewer: Li Changpin (Logan) Cited in 8 Documents MSC: 34A33 Ordinary lattice differential equations 39A12 Discrete version of topics in analysis 34E13 Multiple scale methods for ordinary differential equations 70F45 The dynamics of infinite particle systems 70K70 Systems with slow and fast motions for nonlinear problems in mechanics 70K75 Nonlinear modes 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations Keywords:nonlinear lattice; Hertzian interactions; Newton’s cradle; multiple-scale analysis; discrete \(p\)-Schrödinger equation; breather PDFBibTeX XMLCite \textit{B. Bidégaray-Fesquet} et al., SIAM J. Math. Anal. 45, No. 6, 3404--3430 (2013; Zbl 1292.34008) Full Text: DOI arXiv