dorsal/arxiv
View SchemaNonlinear dynamical systems and classical orthogonal polynomials
| Authors | Krzysztof Kowalski |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9801018 |
| URL | https://arxiv.org/abs/solv-int/9801018 |
| DOI | 10.1063/1.531990 |
| Journal | J. Math. Phys. 38 (1997) 2483-2505 |
Abstract
It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schr\"odinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to the Schr\"odinger equation in the particular occupation number representation are expressed by means of the classical orthogonal polynomials. The introduced formalism amounts a generalization of the classical methods for linearization of nonlinear differential equations such as the Carleman embedding technique and Koopman approach.
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"abstract": "It is demonstrated that nonlinear dynamical systems with analytic\nnonlinearities can be brought down to the abstract Schr\\\"odinger equation in\nHilbert space with boson Hamiltonian. The Fourier coefficients of the expansion\nof solutions to the Schr\\\"odinger equation in the particular occupation number\nrepresentation are expressed by means of the classical orthogonal polynomials.\nThe introduced formalism amounts a generalization of the classical methods for\nlinearization of nonlinear differential equations such as the Carleman\nembedding technique and Koopman approach.",
"arxiv_id": "solv-int/9801018",
"authors": [
"Krzysztof Kowalski"
],
"categories": [
"solv-int",
"nlin.SI",
"quant-ph"
],
"doi": "10.1063/1.531990",
"journal_ref": "J. Math. Phys. 38 (1997) 2483-2505",
"title": "Nonlinear dynamical systems and classical orthogonal polynomials",
"url": "https://arxiv.org/abs/solv-int/9801018"
},
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