孤立波两次反弹共振的力学模拟：建模与实验
A Mechanical Analog of the Two-bounce Resonance of Solitary Waves: Modeling and Experiment
摘要：
我们描述了一个简单的机械系统，一个沿着特别设计的景观滚动的球，它模仿了一个众所周知的现象的动力学，孤波碰撞的两次反弹共振，这已经在无数的数值模拟中看到，但从来没有在实验室中。我们提供了一个简短的历史孤波问题，强调集体坐标模型在理解这种现象中发挥的基本作用。我们推导出控制一个点粒子运动的方程，然后设计一个表面上滚动的球，这样它的运动将演变下的相同的方程，近似控制孤立波碰撞。我们报告的物理实验，进行了本科应用数学课程，似乎验证了一个方面的混沌散射，所谓的双反弹共振。
英文摘要：
We describe a simple mechanical system, a ball rolling along a specially-designed landscape, that mimics the dynamics of a well known phenomenon, the two-bounce resonance of solitary wave collisions, that has been seen in countless numerical simulations but never in the laboratory. We provide a brief history of the solitary wave problem, stressing the fundamental role collective-coordinate models played in understanding this phenomenon. We derive the equations governing the motion of a point particle confined to such a surface and then design a surface on which to roll the ball, such that its motion will evolve under the same equations that approximately govern solitary wave collisions. We report on physical experiments, carried out in an undergraduate applied mathematics course, that seem to verify one aspect of chaotic scattering, the so-called two-bounce resonance.
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