On the heavenly equation hierarchy and its reductions

Details On the heavenly equation hierarchy and its reductions On the heavenly equation hierarchy and its reductions

2005-12-27

arxiv.org/abs/nlin/0512074v2

J.Phys. A39 (2006) 11793-11802

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages, LaTeX, minor misprints corrected, references added

Scientific paper

10.1088/0305-4470/39/38/006

Second heavenly equation hierarchy is considered using the framework of hyper-K\"ahler 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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