A mechanical analog of the two-bounce resonance of solitary waves: Modeling and experiment.
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.
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102.
Roy H
RH
Goodman
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102.
Aminur
A
Rahman
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102.
Michael J
MJ
Bellanich
Veritas Christian Academy, Sparta Township, New Jersey 07871, USA.
Catherine N
CN
Morrison