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- W1657228718 abstract "AbstractA dressing scheme applicable to Dunajski equation is developed.Simple example of constructing solutions in terms of implicit functionsis considered. Dunajski equation hierarchy is described, its Lax-Satoform is presented. Dunajsky equation hierarchy is characterised byconservation of three-dimensional volume form, in which a spectralvariable is taken into account. Some reductions of Dunajsky equationhierarchy, including waterbag-type reduction, are studied. 1 Dunajski equation Dunajski equation [1] is a representative of the class integrable sytems aris-ing in the context of complex relativity [2]-[6]. It is closely connected tothe selebrated Pleban´ski heavenly equations [2] and in some sense general-izes them. It describes anti-self-dual null-Ka¨hler structures. In [1] it wasshown that all null-Ka¨hler metrics (signature (2,2)) locally admit a canonicalPleban´ski formg = dwdx+dzdy −Θ xx dz 2 −Θ yy dw 2 +2Θ xy dwdz. (1)The conformal anti-self-duality (ASD) condition leads to Dunajski equationΘ" @default.
- W1657228718 created "2016-06-24" @default.
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- W1657228718 date "2006-12-20" @default.
- W1657228718 modified "2023-09-27" @default.
- W1657228718 title "On the dressing method for Dunajski anti-self-duality equation" @default.
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