Non-linear Stability of Modulated Fronts for the Swift-Hohenberg Equation

@inproceedings{Eckmann2007NonlinearSO,
  title={Non-linear Stability of Modulated Fronts for the Swift-Hohenberg Equation},
  author={J Eckmann and Guido Schneider},
  year={2007}
}
We consider front solutions of the Swift-Hohenberg equation tu = (1+ 2 x)2u + "2u u3. These are traveling waves which leave in their wake a periodic patt ern in the laboratory frame. Using renormalization techniques and a decomposition into Bloch waves, we show the non -linear stability of these solutions. It turns out that this problem is closely related to the question of stabi li y of the trivial solution for the model problem tu(x; t) = 2 xu(x; t) + (1+ tanh(x t))u(x; t) + u(x; t)p with p… CONTINUE READING