Chaotic scattering in solitary wave interactions: A singular iterated-map description
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102 (United States)
We derive a family of singular iterated maps--closely related to Poincare 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.
- OSTI ID:
- 21100306
- Journal Information:
- Chaos (Woodbury, N. Y.), Vol. 18, Issue 2; Other Information: DOI: 10.1063/1.2904823; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 1054-1500
- Country of Publication:
- United States
- Language:
- English
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