Colliding dissipative pulses-The shooting manifold

Arnd Scheel, J. Douglas Wright

Research output: Contribution to journalArticle

9 Scopus citations

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 x1 and x2, with x1 - x2 ≫ 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.

Original languageEnglish (US)
Pages (from-to)59-79
Number of pages21
JournalJournal of Differential Equations
Volume245
Issue number1
DOIs
StatePublished - Jul 1 2008

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