161 citations · 201 across the 4 of their papers we have counts for
4 papers
Structure Preserving Discretizations of the Liouville Equation and their Numerical Tests
Decio Levi, Luigi Martina, Pavel Winternitz
The main purpose of this article is to show how symmetry structures in partial differential equations can be preserved in a discrete world and reflected in difference schemes. Thre…
An infinite family of solvable and integrable quantum systems on a plane
Frédérick Tremblay, Alexander V. Turbiner, Pavel Winternitz
An infinite family of exactly-solvable and integrable potentials on a plane is introduced. It is shown that all already known rational potentials with the above properties allowing…
Symmetry preserving discretization of SL(2,R) invariant equations
A. Bourlioux, R. Rebelo, P. Winternitz
Nonlinear ODEs invariant under the group SL(2,R) are solved numerically. We show that solution methods incorporating the Lie point symmetries provide better results than standard m…
Polynomial Associative Algebras for Quantum Superintegrable Systems with a Third Order Integral of Motion
Ian Marquette
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the mos…