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On the heavenly equation hierarchy and its reductions

L. V. Bogdanov·B. G. Konopelchenko
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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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L. V. Bogdanov, B. G. Konopelchenko. 2006-01-12. On the heavenly equation hierarchy and its reductions. https://doi.org/10.1088/0305-4470%2F39%2F38%2F006

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