  We extend short-time existence and stability of the Dirichlet energy flow as
proven in a previous paper by the authors to a broader class of energy
functionals. Furthermore, we derive some monotonely decreasing quantities for
the Dirichlet energy flow and investigate an equation of soliton type. In
particular, we show that nearly parallel G_2-structures satisfy this soliton
equation and study their infinitesimal soliton deformations.
