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 psinabla(2)psi and /nablapsi/(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.
Kozyreff
G
G
Optique Nonlinéaire Théorique, Université Libre de Bruxelles (U.L.B.), Campus de la Plaine C.P. 231, Boulevard du Triomphe, B-1050 Bruxelles, Belgium.
Tlidi
M
M
D000465:Algorithms; D001671:Biochemistry / Q000379:methods; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D005246:Feedback / Q000502:physiology*; D008954:Models, Biological; D017711:Nonlinear Dynamics; D055095:Optics and Photonics