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Chaotic scattering in solitary wave interactions: A singular iterated-map description

Chaos 18, 023113 (2008); doi:10.1063/1.2904823

Published 7 May 2008

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Roy H. Goodman
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
We derive a family of singular iterated maps—closely related to Poincaré maps—that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solitary-wave collisions depends on the transfer of energy to a secondary mode of oscillation, often an internal mode of the pulse. This map allows us to go beyond previous analyses and to understand the interactions in the case when this mode is excited prior to the first collision. The map is derived using Melnikov integrals and matched asymptotic expansions and generalizes a “multipulse” Melnikov integral. It allows one to find not only multipulse heteroclinic orbits, but exotic periodic orbits. The maps exhibit singular behavior, including regions of infinite winding. These maps are shown to be singular versions of the conservative Ikeda map from laser physics and connections are made with problems from celestial mechanics and fluid mechanics. ©2008 American Institute of Physics
History: Received 16 October 2007; accepted 7 March 2008; published 7 May 2008
Permalink: http://link.aip.org/link/?CHAOEH/18/023113/1
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KEYWORDS and PACS

Keywords
PACS
  • 05.45.Yv
    Solitons
  • 05.45.-a
    Nonlinear dynamics and chaos
  • 03.75.Lm
    Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations
  • YEAR: 2008

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PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
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REFERENCES (45)
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