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

Roy H. Goodman, Aminur Rahman, Michael J. Bellanich, Catherine N. Morrison

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.

Original languageEnglish (US)
Article number043109
JournalChaos
Volume25
Issue number4
DOIs
StatePublished - Apr 10 2015

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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