Nonlinear dynamical systems and classical orthogonal polynomials

Journal Article · Thu May 01 04:00:00 EDT 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531990· OSTI ID:554238

Kowalski, K ^[1]

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1. Department of Theoretical Physics, University of Lodz, ul. Pomorska 149/153, 90-236 Lodz, (Poland)

It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schr{umlt o}dinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to the Schr{umlt o}dinger equation in the particular occupation number representation are expressed by means of the classical orthogonal polynomials. The introduced formalism amounts to a generalization of the classical methods for linearization of nonlinear differential equations such as the Carleman embedding technique and Koopman approach. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 554238
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 5 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOSONS
DIFFERENTIAL EQUATIONS
DYNAMICS
HILBERT SPACE
NONLINEAR PROBLEMS
POLYNOMIALS
SCHROEDINGER EQUATION