349 citations · 2.2k across the 57 of their papers we have counts for
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Invariant Modules and the Reduction of Nonlinear Partial Differential Equations to Dynamical Systems
Niky Kamran, Robert Milson, Peter Olver
We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant s…
Imprimitively generated Lie-algebraic Hamiltonians and separation of variables
Robert Milson
Turbiner's conjecture posits that a Lie-algebraic Hamiltonian operator whose domain is a subset of the Euclidean plane admits a separation of variables. A proof of this conjecture…
Quantization of cohomology in semi-simple Lie algebras
R. Milson, D. Richter
The space of realizations of a finite-dimensional Lie algebra by first order differential operators is naturally isomorphic to H^1 with coefficients in the module of functions. The…
On the Liouville transformation and exactly-solvable Schrodinger equations
Robert Milson
The present article discusses the connection between exactly-solvable Schrodinger equations and the Liouville transformation. This transformation yields a large class of exactly-so…