caa a22 4500 388108754 CHVBK 20180307125347.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500019387 doi S0308210500019387 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500019387 Essential instability of pulses and bifurcations to modulated travelling waves [Elektronische Daten] Reaction-diffusion systems on the real line are considered. Localized travelling waves become unstable when the essential spectrum of the linearization about them crosses the imaginary axis. In this article, it is shown that this transition to instability is accompanied by the bifurcation of a family of large patterns that are a superposition of the primary travelling wave with steady spatially periodic patterns of small amplitude. The bifurcating patterns can be parametrized by the wavelength of the steady patterns; they are time-periodic in a moving frame. A major difficulty in analysing this bifurcation is its genuinely infinite-dimensional nature. In particular, finite-dimensional Lyapunov-Schmidt reductions or centre-manifold theory do not seem to be applicable to pulses having their essential spectrum touching the imaginary axis. Copyright © Royal Society of Edinburgh 1999 Sandstede B. Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, USA Scheel A. Institut für Mathematik I, Freie Universität Berlin, Arnimallee 2-6, 14195 Berlin, Germany Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/6(1999), 1263-1290 0308-2105 129:6<1263 1999 129 PRM https://doi.org/10.1017/S0308210500019387 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500019387 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sandstede B. Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, USA NATIONALLICENCE 700 1- Scheel A. Institut für Mathematik I, Freie Universität Berlin, Arnimallee 2-6, 14195 Berlin, Germany NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/6(1999), 1263-1290 0308-2105 129:6<1263 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge