Dunajski generalization of the second heavenly equation: dressing method and the hierarchy

Dunajski generalization of the second heavenly equation is studied. A dressing scheme applicable to the Dunajski equation is developed; an example of constructing solutions in terms of implicit functions is considered. A Dunajski equation hierarchy is described, and its Lax-Sato form is presented. The Dunajski equation hierarchy is characterized by the conservation of a three-dimensional volume form, in which a spectral variable is taken into account.