Chaotic Scattering and the $n$-bounce Resonance in Solitary Wave Interactions


We present a new and complete analysis of the n-bounce resonance and chaotic scattering in solitary wave collisions. In these phenomena, the speed at which a wave exits a collision depends in a complicated fractal way on its input speed. We present a new asymptotic analysis of collective-coordinate ODEs, reduced models that reproduce the dynamics of these systems. We reduce the ODEs to discrete-time iterated separatrix maps and obtain new quantitative results unraveling the fractal structure of the scattering behavior. These phenomena have been observed repeatedly in many solitary-wave systems over 25 years.

Physical Review Letters
Roy Goodman
Roy Goodman
Associate Professor, Associate Chair for Graduate Studies, Department of Mathematical Sciences

My research interests include dynamical systems and nonlinear waves, vortex dynamics, quantum graphs, and network inference