349 citations · 1.6k across the 52 of their papers we have counts for
4 papers · 1 filter
The Multidimensional Darboux Transformation
Artemio González-López, Niky Kamran
A generalization of the classical one-dimensional Darboux transformation to arbitrary n-dimensional oriented Riemannian manifolds is constructed using an intrinsic formulation base…
The Lie Algebraic Structure of Differential Operators Admitting Invariant Spaces of Polynomials
Federico Finkel, Niky Kamran
We prove that the scalar and matrix differential operators which preserve the simplest scalar and vector-valued polynomial modules in two variables have a fundamental L…
Real Lie Algebras of Differential Operators and Quasi-Exactly Solvable Potentials
Artemio Gonzalez-Lopez, Niky Kamran, Peter J. Olver
We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensio…
Lie Algebras of Differential Operators and Partial Integrability
Federico Finkel, Artemio Gonzalez-Lopez, Niky Kamran +2
This paper surveys recent work on Lie algebras of differential operators and their application to the construction of quasi-exactly solvable Schroedinger operators.