77 citations · 535 across the 19 of their papers we have counts for
6 papers · 2 filters
Lie symmetries of multidimensional difference equations
Decio Levi, Sébastien Tremblay, Pavel Winternitz
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and o…
Invariants of the nilpotent and solvable triangular Lie algebras
Sébastien Tremblay, Pavel Winternitz
Invariants of the coadjoint representation of two classes of Lie algebras are calculated. The first class consists of the nilpotent Lie algebras , isomorphic to the algebras…
Lie point symmetries of difference equations and lattices
Decio Levi, Sébastien Tremblay, Pavel Winternitz
A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the correspon…
Integrable systems without the Painlevé property
Alfred Ramani, Basile Grammaticos, Sébastien Tremblay
We examine whether the Painlevé property is a necessary condition for the integrability of nonlinear ordinary differential equations. We show that for a large class of linearisable…
Integrable lattice equations and their growth properties
Sébastien Tremblay, Basile Grammaticos, Alfred Ramani
In this paper we investigate the integrability of two-dimensional partial difference equations using the newly developed techniques of study of the degree of the iterates. We show…
On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory
Vladislav Kravchenko, Dominic Rochon, Sebastien Tremblay
Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper we develop a hyperbolic analogue of pseudoanalytic function theory…