Self-dual metrics in Husain's approach
M. Jakimowicz, J. Tafel
TL;DR
This paper demonstrates the equivalence of Husain's reduction of self-dual Einstein equations to the Plebański equation, finds a Bäcklund transformation, and explores contact symmetries and conservation laws.
Contribution
It establishes the equivalence between Husain's approach and the Plebański equation and derives new Bäcklund transformations and symmetries.
Findings
Husain's reduction is equivalent to the Plebański equation
A Bäcklund transformation between the equations is constructed
Contact symmetries and conservation laws are derived
Abstract
We show that Husain's reduction of the self-dual Einstein equations is equivalent to the Pleba\'nski equation. The B\"acklund transformation between these equations is found. Contact symmetries of the Husain-Park equation and corresponding conservation laws are derived.
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