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solv-int1999
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…
solv-int1998
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…
solv-int1998
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…