2007/02/25 by Roy H. Goodman, Goodman, Roy H., Richard Haberman +1 · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Ocean Waves and Remote Sensing #Pattern Formation and Solitons (nlin.PS) #Quantum chaos and dynamical systems #nlin.CD #nlin.PS
paper · pdf · doi:10.48550/arxiv.nlin/0702048
5 pages, 3 figures. Low quality images, see http://m.njit.edu/goodman for high quality images, accepted for publicaiton in Phys. Rev. Lett
arxiv created 2007/02/25 · openalex publication_date 2007/02/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.