Compactons in strongly nonlinear lattices

强非线性晶格中的压子

• 批准号: 19760810
• 负责人: Professor Dr. Arkady Pikovsky
• 金额: --
• 依托单位: Institut für Physik und Astronomie
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2006
• 资助国家: 德国
• 起止时间: 2005-12-31 至 2009-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/19760810?language=en
• 关键词: Compactons; strongly; nonlinear; lattices

The goal of this project is the investigation of localized traveling objects - compactons - in strongly nonlinear lattices. Two particular examples - a chain of phase equations for coupled nonlinear oscillators and a one-dimensional chain of beads under Hertz contact - will be studied in details. We will find a traveling wave in a discrete lattice numerically and compare this solution with that of a quasi-continuum approximation.A perturbative approach for a nonideal lattices will be developed. Collisions of compactons, as well as the long-time properties like transition to chaos, will be investigated numerically.

这个项目的目标是研究强非线性晶格中的局域化运动物体-光子。两个特殊的例子-一个链的耦合非线性振荡器和赫兹接触下的一维链的珠子的相位方程-将详细研究。我们将用数值方法求解离散格点中的行波，并与准连续近似的解进行比较，发展了一种非理想格点的微扰方法。我们将用数值方法研究光子的碰撞，以及向混沌过渡等长时间性质。