Energy functionals and soliton equations for G sub(2)-forms

We extend short-time existence and stability of the Dirichlet energy flow as proven in a previous article 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 sub(2)-structures satisfy this soliton equation and study their infinitesimal soliton deformations.