Numerical simulations of the propagation of ultra-short Gaussian pulses in optical fibers with high-order nonlinearities

Due to the increasing demands for higher channel bitrate continuous pulse shortening is under research. The main goal of this paper is to describe and simulate effects of dispersion and nonlinear phenomena on ultra-short optical pulses propagating through optical fibers. The paper shows that the effect of dispersion causes a frequency shift which can be compensated by self-phase modulation. On the other hand our results prove that effects caused by high-order nonlinearities can be compensated as a result of the third order dispersion which is demonstrated in case of forming the solitary waves.