Chaotic Scattering and the n-Bounce Resonance in Solitary-Wave Interactions

Roy H. Goodman and Richard Haberman
Phys. Rev. Lett. 98, 104103 – Published 9 March 2007

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.

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  • Received 21 August 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.104103

©2007 American Physical Society

Authors & Affiliations

Roy H. Goodman*

  • Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA

Richard Haberman

  • Department of Mathematics, Southern Methodist University, Dallas, Texas 75275, USA

  • *Electronic address: goodman@njit.edu
  • Electronic address: rhaberma@smu.edu

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Vol. 98, Iss. 10 — 9 March 2007

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