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The well-known cubic Allen-Cahn (AC) equation is a simple gradient dynamics(or variational) model for a nonconserved order parameter field. After revisingmain literature results for the occuring different types of moving fronts, weemploy path continuation to determine their bifurcation diagram in dependenceof the external field strength or chemical potential. We then employ the samemethodology to systematically analyse fronts for more involved AC-type models.In particular, we consider a cubic-quintic variational AC model and twodifferent nonvariational generalisations. We determine and compare thebifurcation diagrams of front solutions in the four considered models.

Bifurcations of front motion in passive and active Allen-Cahn-type equations