On the heavenly equation hierarchy and its reductions

Second heavenly equation hierarchy is considered using the framework of hyper-Kähler hierarchy developed by Takasaki [1, 2]. Generating equations for the hierarchy are introduced, they are used to construct generating equations for reduced hierarchies. General N reductions, logarithmic reduction and rational reduction for one of the Lax-Sato functions are discussed. It is demonstrated that rational reduction is equivalent to the symmetry constraint.