A Mechanical Analog of the Two-bounce Resonance of Solitary Waves: Modeling and Experiment

TL;DR

This paper presents a mechanical analog using a ball on a specially designed surface to experimentally demonstrate the two-bounce resonance phenomenon observed in solitary wave collisions, bridging numerical simulations and laboratory experiments.

Contribution

It introduces a simple mechanical system that replicates the complex dynamics of solitary wave interactions, providing the first laboratory demonstration of the two-bounce resonance.

Findings

Experimental verification of two-bounce resonance

Design of a surface that mimics solitary wave collision dynamics

Observation of chaotic scattering behavior

Abstract

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.