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