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Solitary wave collisions
Loss of Physical Reversibility in Reversible Systems
A dynamical system is said to be reversible if, given an output, the input can always be recovered in a well-posed manner. …
Amir Sagiv
,
Adi Ditkowski
,
Roy Goodman
,
Gadi Fibich
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Journal
arXiv
Mathematical Analysis of Fractal Kink-Antikink Collisions in the $\varphi^4$ Model
We analyze the fractal structure seen in kink-antikink collisions of the $\varphi^4$ equation. The analysis is based on qualitative …
Roy Goodman
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arXiv
Book
A Mechanical Analog of the Two-Bounce Resonance of Solitary Waves: Modeling and Experiment
We describe a simple mechanical system, a ball rolling along a specially-designed landscape, that mimics the dynamics of a well known …
Roy Goodman
,
Amin Rahman
,
Michael Bellanich
,
Catherine Morrison
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Journal
arXiv
Chaotic scattering in solitary wave interactions: A singular iterated-map description
We derive a family of singular iterated maps—closely related to Poincaré maps—that describe chaotic interactions between …
Roy Goodman
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Journal
arXiv
Chaotic Scattering and the $n$-bounce Resonance in Solitary Wave Interactions
We present a new and complete analysis of the n-bounce resonance and chaotic scattering in solitary wave collisions. In these …
Roy Goodman
,
Richard Haberman
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Journal
arXiv
Kink-antikink collisions in the $\phi^4$ equation: The $n$-bounce resonance and the separatrix map
We provide a detailed mathematical explanation of a phenomenon known as the two-bounce resonance observed in collisions between kink …
Roy Goodman
,
Richard Haberman
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Journal
Trapping light with grating defects
Gap solitons are localized traveling waves that exist in Bragg grating optical fibers. We demonstrate a family of grating defects that …
Roy Goodman
,
Richart Slusher
,
Michael Weinstein
,
Martin Klaus
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Book
Vector soliton interactions in birefringent optical fibers
We consider the interactions of two identical, orthogonally polarized vector solitons in a nonlinear optical fiber with two …
Roy Goodman
,
Richard Haberman
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Journal
arXiv
Interaction of sine-Gordon kinks with defects: The two-bounce resonance
A model of soliton–defect interactions in the sine-Gordon equations is studied using singular perturbation theory. Melnikov …
Roy Goodman
,
Richard Haberman
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Journal
arXiv
Strong NLS soliton--defect interactions
We consider the interaction of a nonlinear Schrödinger soliton with a spatially localized (point) defect in the medium through which it …
Roy Goodman
,
Phil Holmes
,
Michael Weinstein
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Journal
arXiv
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