A mechanical analog of the two-bounce resonance of solitary waves: Modeling and experiment

Document Type

Article

Publication Date

4-10-2015

Abstract

We describe a simple mechanical system, a ball rolling along a specially-designed landscape, which mimics the well-known two-bounce resonance in solitary wave collisions, a phenomenon 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 exhibit the two-bounce resonance.

Identifier

84927537845 (Scopus)

Publication Title

Chaos

External Full Text Location

https://doi.org/10.1063/1.4917047

e-ISSN

10897682

ISSN

10541500

Issue

4

Volume

25

Grant

0511514

Fund Ref

National Science Foundation

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