Logo image
Back
Colliding dissipative pulses—The shooting manifold
Journal article   Open access   Peer reviewed

Colliding dissipative pulses—The shooting manifold

Arnd Scheel and J. Douglas Wright
Journal of Differential Equations, v 245(1)
2008
DOI: https://doi.org/10.1016/j.jde.2008.03.019
url
https://doi.org/10.1016/j.jde.2008.03.019View
Published, Version of Record (VoR)Open Access (Publisher-Specific),  Open

Abstract

We study multi-pulse solutions in excitable media. Under the assumption that a single pulse is asymptotically stable, we show that there is a well-defined “shooting manifold,” consisting of two pulses traveling towards each other. In phase space, the two-dimensional manifold is a graph over the manifold of linear superpositions of two pulses located at x 1 and x 2 , with x 1 − x 2 ≫ 1 . It is locally invariant under the dynamics of the reaction–diffusion system and uniformly asymptotically attracting with asymptotic phase. The main difficulty in the proof is the fact that the linearization at the leading order approximation is strongly non-autonomous since pulses approach each other with speed of order one.

Metrics

14 Record Views
9 citations in Web of Science
11 citations in Scopus

Details

InCites Highlights

Data related to this publication, from InCites Benchmarking & Analytics tool:

Collaboration types
Domestic collaboration
Web of Science research areas
Mathematics
Logo image