Chaotic scattering and the n-bounce resonance in solitary-wave interactions

Roy H. Goodman, Richard Haberman

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61 Scopus citations

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 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.

Original languageEnglish (US)
Article number104103
JournalPhysical Review Letters
Volume98
Issue number10
DOIs
StatePublished - Mar 9 2007

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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