Propagation of ultrashort pulses through a nonresonance quadratically nonlinear medium in the unidirectional wave approximation

The propagation and interaction of ultrashort pulses in a nonresonance quad ratically nonlinear medium is considered. A stationary solution was found a nalytically. It was demonstrated numerically that pulses with an energy muc h lower than the energy of a stationary pulse decay under the influence of dispersion during propagation, whereas pulses with an energy higher than th e energy of a stationary pulse disintegrate into a series of pulses moving like stationary ones. The effect of additive and multiplicative amplitude m odulation on the pulse propagation was investigated. Stationary pulses were shown to be stable upon weak modulation and in collisions with each other.