Localized and extended patterns in the cubic-quintic Swift-Hohenberg equation on a disk

Swift-Hohenberg equation with broken cubic-quintic nonlinearity.

The cubic-quintic Swift-Hohenberg equation (SH35) provides a convenient order parameter description of several convective systems with reflection symmetry in the layer midplane, including binary fluid convection. We use SH35 with an additional quadratic term to determine the qualitative effects of breaking the midplane reflection symmetry on the properties of spatially localized structures in t...

Localized Hexagon Patterns of the Planar Swift-Hohenberg Equation

We investigate stationary spatially localized hexagon patterns of the two-dimensional (2D) Swift– Hohenberg equation in the parameter region where the trivial state and regular hexagon patterns are both stable. Using numerical continuation techniques, we trace out the existence regions of fully localized hexagon patches and of planar pulses which consist of a strip filled with hexagons that is ...

Exact solutions of the cubic–quintic Swift–Hohenberg equation and their bifurcations

Snakes and Ladders: localized states in the Swift-Hohenberg equation

Stable spatially localized structures occur in many systems of physical interest. Examples can be found in the fields of optics, chemistry, fluid mechanics, and neuroscience to name a few. The models used to describe these systems have much in common. They are typically of at least fourth order in spatial derivatives, invariant under spatial translations and reflections, and exhibit bistability...

Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity.

The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a variety of spatially localized structures, in addition to different spatially extended periodic structures. The location of these structures in the temperature v...