从牛顿摆到离散p-薛定谔方程
From Newton's cradle to the discrete p-Schrödinger equation
摘要：
本文研究了由完全非线性相互作用势耦合的振子链的动力学。这类模型包括牛顿摆与赫兹接触的相互作用的邻居。通过多尺度分析，我们给出了小振幅解在大时间上的严格渐近描述。导致近似解的包络方程是离散的p-薛定谔方程。我们的结果包括存在的长寿呼吸原模型的解决方案。对于一个大类的本地化的初始条件，我们还估计了最大衰减的小振幅的解决方案在很长一段时间。
英文摘要：
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.
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