Dunajski generalization of the second heavenly equation: dressing method and the hierarchy

Abstract

Dunajski generalization of the second heavenly equation is studied. A dressing scheme applicable to Dunajski equation is developed, an example of constructing solutions in terms of implicit functions is considered. Dunajski equation hierarchy is described, its Lax-Sato form is presented. Dunajsky equation hierarchy is characterized by conservation of three-dimensional volume form, in which a spectral variable is taken into account.

13 pages

References in corpus (2)

• Inverse Scattering Problem for Vector Fields and the Cauchy Problem for the Heavenly Equation
• On the heavenly equation hierarchy and its reductions

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