Derivation of kinetic equation for model system with discrete spectrum without the hypothesis of correlation damping

Behaviour of the nonlinear oscillator interacting with a discrete oscillator system is studied without taking into account the response effect on the system. It is shown that the character of the oscillator motion is determined by the stochastic parameter $K$. The method is given for constructing the solution as the series over the powers of $K$ for $K\ll 1$ and $K^{-1}$ for $K\gg 1$ which describe the motion of the system in the stable and stochastic cases, respectively. In the case $K\gg 1$ a kinetic equation was obtained; the behaviour of the harmonics of distribution function and two-particle correlator was studied and the character of correlation splitting was also investigated. Transition to the linear case is discussed.