Nonvariational real Swift-Hohenberg equation for biological, chemical, and optical systems

We derive asymptotically an order parameter equation in the limit where nascent bistability and long-wavelength modulation instabilities coalesce. This equation is a variant of the Swift-Hohenberg equation that generally contains nonvariational terms of the form ψ ∇ 2 ψ and ∣ ∇ ψ ∣ 2 . We briefly review some of the properties already derived for this equation and derive it on three examples taken from chemical, biological, and optical contexts. Finally, we derive the equation on a general class of partial differential systems.