26 citations · 116 across the 10 of their papers we have counts for
9 papers · 1 filter
Recursion operators and bi-Hamiltonian structure of the general heavenly equation
M. B. Sheftel, A. A. Malykh, D. Yazıcı
We discover two additional Lax pairs and three nonlocal recursion operators for symmetries of the general heavenly equation introduced by Doubrov and Ferapontov. Converting the equ…
Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors
Mikhail B. Sheftel, Andrei A. Malykh
We demonstrate how a combination of our recently developed methods of partner symmetries, symmetry reduction in group parameters and a new version of the group foliation method can…
General heavenly equation governs anti-self-dual gravity
A. A. Malykh, M. B. Sheftel
We show that the general heavenly equation, suggested recently by Doubrov and Ferapontov \cite{fer}, governs anti-self-dual (ASD) gravity. We derive ASD Ricci-flat vacuum metric go…
Recursions of Symmetry Orbits and Reduction without Reduction
Andrei A. Malykh, Mikhail B. Sheftel
We consider a four-dimensional PDE possessing partner symmetries mainly on the example of complex Monge-Ampère equation (CMA). We use simultaneously two pairs of symmetries related…
On a class of second-order PDEs admitting partner symmetries
M. B. Sheftel, A. A. Malykh
Recently we have demonstrated how to use partner symmetries for obtaining noninvariant solutions of heavenly equations of Plebanski that govern heavenly gravitational metrics. In t…
Lift of Invariant to Non-Invariant Solutions of Complex Monge-Ampère Equations
M. B. Sheftel, A. A. Malykh
We show how partner symmetries of the elliptic and hyperbolic complex Monge-Ampère equations (CMA and HCMA) provide a lift of non-invariant solutions of three- and two-dimensional…