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 ordinary differential equations (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.
Goodman
Roy H
RH
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA. goodman@njit.edu
Haberman
Richard
R