1. Jan 24, 2010

zetafunction

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

where f(u) is an smooth function , u=U(x,t) is the solution of the PDE

this is the Swift-Hohenberg equation, my teacher has asked me to solve it or look some info about it specially

- How it can be solved by Analytic methods in 1-D (x,t)

- Special cases: spherical, cilindric coordinates

i heard it was compeltely known how to solve (approximately) this equation, could someone give me some info about how the S-H is deduced mathematically and how to find the solutions for several f(u) ?? .. thanks in advance.