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

Document Type

Article

Publication Date

1-1-2008

Abstract

We derive a family of singular iterated maps-closely related to Poincaŕ 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.

Identifier

46449139328 (Scopus)

Publication Title

Chaos

External Full Text Location

https://doi.org/10.1063/1.2904823

ISSN

10541500

Issue

2

Volume

18

Grant

DMS-0506495

Fund Ref

National Science Foundation

This document is currently not available here.

Share

COinS