A nonlinear oscillation model with separation of variables

Yu. I. Kuznetsov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences

Abstract: This paper deals with one-dimensional and two-dimensional oscillatory systems. The theorem about separation of spatial and time variables for this problem is proved. The ODE system for the Fourier coefficients of the solution was found. Numerical experiments with a one-dimensional oscillatory system point to the existence of other oscillations – the energy oscillations inside some cluster of harmonics.

Key words: nonlinear, the oscillation systems, one-dimensional, two-dimensional, Kronecker product, ODE system, separation of variables, clusters of harmonics, energy oscillations, approximant.

UDC: 517.518.36

Received: 14.08.2006
Revised: 27.12.2006