Invariant Modules and the Reduction of Nonlinear Partial Differential Equations to Dynamical Systems

Preprint

15 April 1999

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.solv-int/9904014

Abstract

We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical partial differential equations to a system of ordinary differential equations, and provide a nonlinear counterpart to quasi-exactly solvable quantum Hamiltonians. These results rely on a useful extension of the classical Wronskian determinant condition for linear independence of functions. In addition, new approaches to the characterization o f the annihilating differential operators for spaces of analytic functions are presented.

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