Chaotic Scattering and the $n$-bounce Resonance in Solitary Wave Interactions
Abstract
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.
Keywords
Cite
@article{arxiv.nlin/0702048,
title = {Chaotic Scattering and the $n$-bounce Resonance in Solitary Wave Interactions},
author = {Roy H. Goodman and Richard Haberman},
journal= {arXiv preprint arXiv:nlin/0702048},
year = {2007}
}
Comments
5 pages, 3 figures. Low quality images, see http://m.njit.edu/goodman for high quality images, accepted for publicaiton in Phys. Rev. Lett