On the propagation of plane multi-band spectrum electromagnetic waves in weakly nonlinear media

A theory is developed for the propagation of plane electromagnetic waves with a narrow-band spectrum in weakly nonlinear media. Representation of a wave as a set of harmonics with slowly spatially-varying amplitudes and spectrum parameters allows us to obtain evolutionary equations for these parameters. This yields a description of energy migration between harmonics, and also their spectrum and wave-envelopes transformation. Forming of harmonic pulses (spectra) in the near zone and the asymptotic behavior in the far zone, including conditions of pulses compression (or stretching) are investigated.