Anomalous Dispersion and Pulse Interaction in an Excitable Surface Reaction

We describe a novel nucleation mechanism of scroll rings in three-dimensional reaction-diffusion systems with anomalous dispersion. The vortices form after the collision of two spherical wave fronts from a third, trailing wave that only partially annihilates in the wake of its predecessor. Depending on the relative positions of the three relevant wave sources, one obtains untwisted or twisted scroll rings. The formation of both vortex structures is demonstrated for a modified Belousov-Zhabotinsky reaction.

mentioning

confidence: 99%

Nucleation and Collapse of Scroll Rings in Excitable Media

Bánsági

Steinbock²

2006

“…Motivation.-Bound states of solitons and solitary pulses are attracting increasing attention in nonlinear optics [1][2][3][4][5], dynamics of fluids [6][7][8][9], and excitable media [10]. Stable bound states can compete with free solitons as alternative attractors.…”

mentioning

confidence: 99%

Stable Complexes of Parametrically Driven, Damped Nonlinear Schrödinger Solitons

Barashenkov

Zemlyanaya

1999

Since solitons of the parametrically driven damped nonlinear Schrödinger equation do not have oscillatory tails, it was suggested that they cannot form bound states. We show that this equation does support solitonic complexes, with the mechanism of their formation being different from the standard tail-overlap mechanism. One of the arising stationary complexes is found to be stable in a wide range of parameters, others unstable. PACS numbers: 42.65.Tg, 05.45.Yv Motivation.-Bound states of solitons and solitary pulses are attracting increasing attention in nonlinear optics [1-5], dynamics of fluids [6-9], and excitable media [10]. Stable bound states can compete with free solitons as alternative attractors. This is detrimental in nonlinear optics, for example, where the interaction between adjacent pulses poses limitations to the stable operation of transmission lines and information storage elements. Unstable solitonic complexes are not meaningless either; they serve as intermediate states visited by the system when in the spatiotemporal chaotic regime.Here, we consider solitonic complexes in the parametrically driven damped nonlinear Schrödinger equation,

“…Indications for anomalous dispersion have been found in natural systems, for example, in experiments on chemical waves that organize the early stages of aggregation in the life cycle of the cellular slime mold Dictyostelium discoideum [7] and in the reduction of NO with CO on Pt(100) surfaces [8].…”

mentioning

confidence: 99%

Oscillatory Dispersion and Coexisting Stable Pulse Trains in an Excitable Medium

Bordiougov

Engel

2003

For planar wave trains in excitable media, we found a novel type of anomalous dispersion distinguished by bistable domains in the dependence of the propagation velocity on the wavelength. Within one medium alternative stable pulse trains can coexist having the same wavelength but different velocities. The phenomenon is related to oscillatory recovery of excitations, which causes small amplitude oscillations in the refractory tail of pulses. Crucial for the bistability is that the pulses in the trains are locked into one oscillation maximum in the tail of the preceding pulse in the train.