Pattern selection for two breathers

Tsutomu Ikeda, Yasumasa Nishiura

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

This paper is devoted to the study of pattern selection problems among two different types of layer-oscillating solutions (in-phase and out-of-phase breathers) of reaction-diffusion systems. εtauUt=epsilon2Uxx+f(u,v), vt =vxx+g(u,v) involving two parameters 0 < ε ≪ 1 and τ > 0. It is shown that the selected pattern, i.e. , stable observable solution, strongly depends on the location of internal layers. Especially for sufficiently small ε, the shift of pattern selection occurs arbitrarily many times from in-phase to out-of-phase, or vice versa, when two layers approach the boundary separately, while the only observable oscillation mode is out-of-phase when two layers come close.

Original languageEnglish
Pages (from-to)195-230
Number of pages36
JournalSIAM Journal on Applied Mathematics
Volume54
Issue number1
DOIs
Publication statusPublished - 1994 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Applied Mathematics

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