Nonlinear dynamical systems and classical orthogonal polynomials

It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schrodinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to the Schrodinger 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. (C) 1997 American institute of Physics.