Article révisé par les pairs
Résumé : 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. © 2007 American Institute of Physics.