Publications (53)
All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1
Libor Snobl, Pavel Winternitz
We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find…
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…
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…
Separation of variables and Lie algebra contractions. Applications to special functions
George Pogosyan, Alexey Sissakian, Pavel Winternitz
A review is given of some recently obtained results on analytic contractions of Lie algebras and Lie groups and their applications to special function theory.
Reduction of superintegrable systems: the anisotropic harmonic oscillator
Miguel A. Rodriguez, Piergiulio Tempesta, Pavel Winternitz
We introduce a new 2N--parametric family of maximally superintegrable systems in N dimensions, obtained as a reduction of an anisotropic harmonic oscillator in a 2N--dimensional co…
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…