Nonlinear dynamical systems and classical orthogonal polynomials

Details Nonlinear dynamical systems and classical orthogonal polynomials Nonlinear dynamical systems and classical orthogonal polynomials

1998-01-14

arxiv.org/abs/solv-int/9801018v1

J. Math. Phys. 38 (1997) 2483-2505

Nonlinear Sciences

Exactly Solvable and Integrable Systems

21 pages latex, uses revtex

Scientific paper

10.1063/1.531990

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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