Self-modulation of optical pulses in a Kerr medium and limits of the single-mode approximation

The formal definition of the effective oscillator is suggested. The propaga tion of an optical pulse in a Kerr medium is formulated in terms of the eff ective oscillators. Limits of the single-mode approximation are discussed. It is shown that the number of photons escaped from the principal mode to t he highest modes is much greater than the square of the nonlinear phase shi ft of the principal mode. This prohibits the production of the "Schodinger cat" states by nonlinear automodulation of the coherent rectangular optical pulses in a Kerr medium, but allows the squeezing.