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Chaotic scattering in solitary wave interactions: a singular iterated-map description.
1Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
Chaos (Woodbury, N.Y.)
|July 8, 2008
Summary
We developed new singular iterated maps to model chaotic solitary wave collisions. These maps reveal energy transfer dynamics and enable analysis of previously unstudied pre-excited internal modes.
Area of Science:
- Nonlinear Dynamics and Chaos Theory
- Soliton Physics
- Mathematical Physics
Background:
- Solitary wave collisions can exhibit chaotic behavior due to energy transfer to secondary oscillation modes.
- Previous analyses were limited, particularly when internal modes are excited before the first collision.
Purpose of the Study:
- To derive a novel family of singular iterated maps describing chaotic solitary wave interactions.
- To extend the understanding of solitary wave collisions, including cases with pre-excited internal modes.
Main Methods:
- Derivation of singular iterated maps using Melnikov integrals and matched asymptotic expansions.
- Generalization of multipulse Melnikov integrals to analyze complex orbit structures.
Main Results:
- The derived maps accurately describe chaotic interactions between colliding solitary waves.
- Singular behavior, including infinite winding regions, was observed in the maps.
- The maps are identified as singular versions of the conservative Ikeda map.
Conclusions:
- The new maps provide a powerful tool for analyzing chaotic solitary wave dynamics.
- The study offers insights into exotic periodic and multipulse heteroclinic orbits.
- Connections are established with problems in laser physics, celestial mechanics, and fluid mechanics.
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