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Structure theorems for linear and non-linear differential operators admitting invariant polynomial subspaces

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Gómez-Ullate Otaiza, David and Kamran, Niky and Milson, Robert (2007) Structure theorems for linear and non-linear differential operators admitting invariant polynomial subspaces. Discrete and continuous dynamical systems, 18 (1). pp. 85-106. ISSN 1078-0947

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Official URL: http://dx.doi.org/10.3934/dcds.2007.18.85




Abstract

In this paper we derive structure theorems which characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful concept of deficiency, we can write an explicit basis for these spaces of differential operators. In the case of linear operators, these results apply to the theory of quasi-exact solvability in quantum mechanics, especially in the multivariate case where the Lie algebraic approach is harder to apply. In the case of non-linear operators, the structure theorems in this paper can be applied to the method of finding special solutions of non-linear evolution equations by nonlinear separation of variables.


Item Type:Article
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© American Institute of Mathematical Sciences.

Uncontrolled Keywords:Diffusion-equations; Calogero; Algebras; Spaces
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:30879
Deposited On:15 Jun 2015 09:33
Last Modified:10 Dec 2018 15:09

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