224 citations · 2.5k across the 74 of their papers we have counts for
48 papers · 1 filter
Superintegrable systems with spin and second-order (pseudo)tensor integrals of motion
I. Yurdusen, O. O. Tuncer, P. Winternitz
We investigate a quantum non-relativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. Assuming that the Hamiltonian is rotationally i…
New infinite families of th-order superintegrable systems separating in Cartesian coordinates
A. M. Escobar-Ruiz, R. Linares, P. Winternitz
A study is presented of superintegrable quantum systems in two-dimensional Euclidean space allowing the separation of variables in Cartesian coordinates. In addition to the H…
Higher Order Quantum Superintegrability: a new "Painlevé conjecture"
Ian Marquette, Pavel Winternitz
We review recent results on superintegrable quantum systems in a two-dimensional Euclidean space with the following properties. They are integrable because they allow the separatio…
Two-dimensional superintegrable systems from operator algebras in one dimension
Ian Marquette, Masoumeh Sajedi, Pavel Winternitz
We develop new constructions of 2D classical and quantum superintegrable Hamiltonians allowing separation of variables in Cartesian coordinates. In classical mechanics we start fro…
Fourth-order superintegrable systems separating in Polar Coordinates. II. Standard Potentials
A. M. Escobar-Ruiz, J. C. López Vieyra, P. Winternitz +1
Superintegrable Hamiltonian systems in a two-dimensional Euclidean space are considered. We present all real standard potentials that allow separation of variables in polar coordin…
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…
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…
The Korteweg-de Vries equation and its symmetry-preserving discretization
Alexander Bihlo, Xavier Coiteux-Roy, Pavel Winternitz
The Korteweg-de Vries equation is one of the most important nonlinear evolution equations in the mathematical sciences. In this article invariant discretization schemes are constru…
Classical and Quantum Superintegrability with Applications
Willard Miller, Sarah Post, Pavel Winternitz
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and qua…
First integrals of ordinary difference equations which do not possess a variational formulation
P. Winternitz, V. Dorodnitsyn, E. Kaptsov +1
The paper presents a new method for finding first integrals of ordinary difference equations which do not possess Lagrangians, nor Hamiltonians. As an example we solve a third orde…
Lie groups and numerical solutions of differential equations: Invariant discretization versus differential approximation
Decio Levi, Pavel Winternitz
We briefly review two different methods of applying Lie group theory in the numerical solution of ordinary differential equations. On specific examples we show how the symmetry pre…
Superintegrable systems with spin and second-order integrals of motion
Jean-Francois Desilets, Pavel Winternitz, Ismet Yurdusen
We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally i…
Infinite families of superintegrable systems separable in subgroup coordinates
Daniel Lévesque, Sarah Post, Pavel Winternitz
A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is…
Contact transformations for difference schemes
Decio Levi, Zora Thomova, Pavel Winternitz
We define a class of transformations of the dependent and independent variables in an ordinary difference scheme. The transformations leave the solution set of the system invariant…
Solvable Lie algebras with Borel nilradicals
Libor Snobl, Pavel Winternitz
The present article is part of a research program the aim of which is to find all indecomposable solvable extensions of a given class of nilpotent Lie algebras. Specifically in thi…
Are there Contact Transformations for Discrete Equations?
Decio Levi, Zora Thomova, Pavel Winternitz
We define infinitesimal contact transformations for ordinary difference schemes as transformations that depend on lattice points and can be integrated to form a…
A nonseparable quantum superintegrable system in 2D real Euclidean space
Sarah Post, Pavel Winternitz
In this paper, we derive a nonseparable quantum superintegrable system in 2D real Euclidean space. The Hamiltonian admits no second order integrals of motion but does admit one thi…
An infinite family of superintegrable deformations of the Coulomb potential
S. Post, P. Winternitz
We introduce a new family of Hamiltonians with a deformed Kepler- Coulomb potential dependent on an indexing parameter k. We show that this family is superintegrable for all ration…
Third order superintegrable systems separating in polar coordinates
Frederick Tremblay, Pavel Winternitz
A complete classification is presented of quantum and classical superintegrable systems in that allow the separation of variables in polar coordinates and admit an additional…
Periodic orbits for an infinite family of classical superintegrable systems
Frédérick Tremblay, Alexander V. Turbiner, Pavel Winternitz
We show that all bounded trajectories in the two dimensional classical system with the potential $V(r,ϕ)=ω^2 r^2+ \frac{\al k^2}{r^2 \cos^2 {k ϕ}}+ \frac{βk^2}{r^2 \sin^2 {k ϕ}}$ a…
Symmetry reduction and superintegrable Hamiltonian systems
M. A. Rodriguez, P. Tempesta, P. Winternitz
We construct complete sets of invariant quantities that are integrals of motion for two Hamiltonian systems obtained through a reduction procedure, thus proving that these systems…