On the heavenly equation hierarchy and its reductions

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.

13 pages, LaTeX, minor misprints corrected, references added

References in corpus (8)

• Einstein-Weyl geometry, the dKP equation and twistor theory
• A class of Einstein--Weyl spaces associated to an integrable system of hydrodynamic type
• Hyper-K{ä}hler Hierarchies and their twistor theory
• Hydrodynamic reductions of multi-dimensional dispersionless PDEs: the test for integrability
• Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type
• On the dbar-dressing method applicable to heavenly equation
• Hydrodynamic reductions of the heavenly equation
• Nonlinear Beltrami equation and tau-function for dispersionless hierarchies

Cited by in corpus (4)

• On the integrability of symplectic Monge-Ampére equations
• Dunajski generalization of the second heavenly equation: dressing method and the hierarchy
• Recursion operators for dispersionless integrable systems in any dimension
• On the Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems