132 citations · 368 across the 13 of their papers we have counts for
6 papers · 1 filter
The Swift-Hohenberg equation with a nonlocal nonlinearity
David Morgan, Jonathan H. P. Dawes
It is well known that aspects of the formation of localised states in a one-dimensional Swift--Hohenberg equation can be described by Ginzburg--Landau-type envelope equations. This…
Variational approximation and the use of collective coordinates
J. H. P. Dawes, H. Susanto
We consider propagating, spatially localised waves in a class of equations that contain variational and non-variational terms. The dynamics of the waves is analysed through a colle…
Snaking and isolas of localised states in bistable discrete lattices
Chris Taylor, Jonathan H. P. Dawes
We consider localised states in a discrete bistable Allen-Cahn equation. This model equation combines bistability and local cell-to-cell coupling in the simplest possible way. The…
Snaking and isolas of localized states in bistable discrete lattices
Christopher R. N. Taylor, Jonathan H. P. Dawes
We consider localized states in a discrete bistable Allen-Cahn equation. This model equation combines bistability and local cell-to-cell coupling in the simplest possible way. The…
Resonance bifurcations from robust homoclinic cycles
Claire M Postlethwaite, Jonathan H P Dawes
We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbo…
Instabilities induced by a weak breaking of a strong spatial resonance
J. H. P. Dawes, C. M. Postlethwaite, M. R. E. Proctor
Through multiple-scales and symmetry arguments we derive a model set of amplitude equations describing the interaction of two steady-state pattern-forming instabilities, in the cas…