On the heavenly equation hierarchy and its reductions
L. V. Bogdanov, B. G. Konopelchenko
Abstract
Second heavenly equation hierarchy is considered using the framework of hyper-Kähler hierarchy developed by Takasaki. 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.
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