Non-linear differential operators with invariant subspaces

Niky Kamran (nkamran@math.mcgill.ca)
Department of Mathematics and Statistics
McGill University
805 Sherbrooke Street West
Montreal, QC H3A 2K6

Abstract
We completely characterize the non-linear differential operators leaaving invariant a given regular finite-dimensional vector space of analytic functions. The existence of an invariant subspace leads to a reduction of the associated evolution equations to a system of ordinary differential equations and provides a non-linear counterpart to quasi-exactly solvable quantum Hamiltonians.