When weakly coupling the classical one-dimensional Allen-Cahn interface model to large scale fields, the dynamics drastically changes. For linear coupling this can be rigorously analysed in a rather explicit way. Combining various methods from spatial dynamics and dynamical systems allows to detect and unfold degenerate Takens-Bodganov points for the interface dynamics. This features various periodic, homoclinic and heteroclinic solutions.
This is joint work with Martina Chirilus-Bruckner, Peter van Heijster and Hideo Ikeda.