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.
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