Swift-Hohenberg equation

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The Swift-Hohenberg equation is a partial differential equation noted for its pattern-forming behaviour. It takes the form

\frac{\partial u}{\partial t} = r u - (1+\nabla^2)^2u + N(u)

where u = u(x, t) or u = u(x, y, t) is a scalar function defined on the line or the plane, r is a real bifurcation parameter, and N(u) is some smooth nonlinearity.

The webpage of Michael Cross[1] contains some numerical integrators which demonstrate the behaviour of several Swift-Hohenberg-like systems.

[edit] References

  1. ^ Java applet demonstrations
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