dorsal/arxiv
View SchemaInvariant Modules and the Reduction of Nonlinear Partial Differential Equations to Dynamical Systems
| Authors | Niky Kamran, Robert Milson, Peter Olver |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9904014 |
| URL | https://arxiv.org/abs/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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"abstract": "We completely characterize all nonlinear partial differential equations\nleaving a given finite-dimensional vector space of analytic functions\ninvariant. Existence of an invariant subspace leads to a re duction of the\nassociated dynamical partial differential equations to a system of ordinary\ndifferential equations, and provide a nonlinear counterpart to quasi-exactly\nsolvable quantum Hamiltonians. These results rely on a useful extension of the\nclassical Wronskian determinant condition for linear independence of functions.\nIn addition, new approaches to the characterization o f the annihilating\ndifferential operators for spaces of analytic functions are presented.",
"arxiv_id": "solv-int/9904014",
"authors": [
"Niky Kamran",
"Robert Milson",
"Peter Olver"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Invariant Modules and the Reduction of Nonlinear Partial Differential Equations to Dynamical Systems",
"url": "https://arxiv.org/abs/solv-int/9904014"
},
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