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Propagation of hexagonal patterns near onset

  • ARJEN DOELMAN (a1), BJÖRN SANDSTEDE (a2), ARND SCHEEL (a3) and GUIDO SCHNEIDER (a4)

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.

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Propagation of hexagonal patterns near onset

  • ARJEN DOELMAN (a1), BJÖRN SANDSTEDE (a2), ARND SCHEEL (a3) and GUIDO SCHNEIDER (a4)

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