224 citations · 2.5k across the 74 of their papers we have counts for
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math-ph2005★ 26 cited
Discretization of partial differential equations preserving their physical symmetries
Francis Valiquette, Pavel Winternitz
A procedure for obtaining a "minimal" discretization of a partial differential equation, preserving all of its Lie point symmetries is presented. "Minimal" in this case means that…
nlin.SI2005★ 116 cited
Continuous Symmetries of Difference Equations
D. Levi, P. Winternitz
Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much m…
math-ph2005★ 1 cited
Quasiseparation of variables in the Schroedinger equation with a magnetic field
F. Charest, C. Hudon, P. Winternitz
We consider a two-dimensional integrable Hamiltonian system with a vector and scalar potential in quantum mechanics. Contrary to the case of a pure scalar potential, the existence…