Propagation of hexagonal patterns near onset

Arjen Doelman, Björn Sandstede, Arnd Scheel, Guido Schneider

Research output: Contribution to journalArticlepeer-review

43 Scopus citations

Abstract

For a pattern-forming system with two unbounded spatial directions that is near the onset to instability, we prove the existence of modulated fronts that connect (i) stable hexagons with the unstable trivial pattern, (ii) stable hexagons with unstable roll solutions, (iii) stable hexagons with unstable hexagons, and (iv) stable roll solutions with unstable hexagons. Our approach is based on spatial dynamics, bifurcation theory, and geometric singular perturbation theory.

Original languageEnglish (US)
Pages (from-to)85-110
Number of pages26
JournalEuropean Journal of Applied Mathematics
Volume14
Issue number1
DOIs
StatePublished - Feb 2003

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