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

✍ Scribed by Niky Kamran; Robert Milson; Peter J. Olver

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 228 KB
Volume: 156
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.2000.1953

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✦ Synopsis

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 reduction of the associated dynamical partial differential equations to a system of ordinary differential equations and provides 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 of the annihilating differential operators for spaces of analytic functions are presented.

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