I am having trouble solving a 4th-order nonlinear PDE ("Swift-Hohenberg equation"). I understand that higher-order derivatives are problem and tried to write it as a two second-order equations, with periodic boundary conditions. It hangs (see attached notebook). I tried various options within NDSolveValue (e.g., method of lines) but did not get a different result.

Is there a way to solve this equation in Mathematica? I have seen matlab code for a solution using spectral methods (Fourier transform the linear spatial terms, then solve numerically the ODE in time), but this would be a more involved program.

Ideas? (My real goal, by the way, is to solve a generalization of this equation to 2 spatial dimensions....)