Swift–Hohenberg equation
The Swift–Hohenberg equation is a partial differential equation noted for its pattern-forming behaviour. It takes the form
where u = u or u = u is a scalar function defined on the line or the plane, r is a real bifurcation parameter, and N is some smooth nonlinearity.
The equation is named after the authors of the paper, where it was derived from the equations for thermal convection.
The webpage of Michael Cross contains some numerical integrators which demonstrate the behaviour of several Swift–Hohenberg-like systems.Applications
In 2009 Ruggero Gabbrielli published a way to use the Swift-Hohenberg equation to find candidate solutions to the Kelvin Problem on minimal surfaces.
