120 citations
6 papers
Recursion operators for vacuum Einstein equations with symmetries
M. Marvan
Direct and inverse recursion operator is derived for the vacuum Einstein equations for metrics with two commuting Killing vectors that are orthogonal to a foliation by 2-dimensiona…
The functional formulation of second-order ordinary differential equations
P. Chladek
In this paper, the necessary and sufficient conditions in order that a smooth mapping F be a dependence of a complete solution of some second-order ordinary differential equation o…
On bosonic limits of two recent supersymmetric extensions of the Harry Dym hierarchy
S. Yu. Sakovich
Two generalized Harry Dym equations, recently found by Brunelli, Das and Popowicz in the bosonic limit of new supersymmetric extensions of the Harry Dym hierarchy [J. Math. Phys. 4…
Transformation of a generalized Harry Dym equation into the Hirota--Satsuma system
S. Yu. Sakovich
The new generalized Harry Dym equation, recently introduced by Z. Popowicz in Phys. Lett. A 317, 260--264 (2003), is transformed into the Hirota--Satsuma system of coupled KdV equa…
Equatorial circular orbits in the Kerr-de Sitter spacetimes
Z. Stuchlik, P. Slany
Equatorial motion of test particles in the Kerr-de Sitter spacetimes is considered. Circular orbits are determined, their properties are discussed for both the black-hole and naked…
Locality of symmetries generated by nonhereditary, inhomogeneous, and time-dependent recursion operators: a new application for formal symmetries
Artur Sergyeyev
Using the methods of the theory of formal symmetries, we obtain new easily verifiable sufficient conditions for a recursion operator to produce a hierarchy of local generalized sym…