224 citations · 2.5k across the 74 of their papers we have counts for
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Linear or linearizable first-order delay ordinary differential equations and their Lie point symmetries
Vladimir A. Dorodnitsyn, Roman Kozlov, Sergey V. Meleshko +1
A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs.…
Lie group classification of first-order delay ordinary differential equations
Vladimir A. Dorodnitsyn, Roman Kozlov, Sergey V. Meleshko +1
A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for delay parameter (delay relation) is presented. A subset of such sys…
Fifth-order superintergrable quantum system separating in Cartesian coordinates. Doubly exotic potentials
Ismail Abouamal, Pavel Winternitz
We consider a two dimensional quantum Hamiltonian separable in Cartesian coordinates and allowing a fifth-order integral of motion. We impose the superintegrablity condition and fi…
Fourth order superintegrable systems separating in Polar Coordinates. I. Exotic Potentials
Adrian M. Escobar-Ruiz, J. C. López Vieyra, P. Winternitz
We present all real quantum mechanical potentials in a two-dimensional Euclidean space that have the following properties: 1. They allow separation of variables of the Schrödinger…
Conformally invariant elliptic Liouville equation and its symmetry preserving discretization
Decio Levi, Luigi Martina, Pavel Winternitz
The symmetry algebra of the real elliptic Liouville equation is an infinite-dimensional loop algebra with the simple Lie algebra as its maximal finite-dimensional subalgeb…
Fourth order Superintegrable systems separating in Cartesian coordinates I. Exotic quantum potentials
Ian Marquette, Masoumeh Sajedi, Pavel Winternitz
A study is presented of two-dimensional superintegrable systems separating in Cartesian coordinates and allowing an integral of motion that is a fourth order polynomial in the mome…