Abstract
The nonlinear Schrödinger equation (NSE) is well-known and is one of the most commonly used in the field of nonlinear optics. Pulses with picosecond and femtosecond duration are very well described by the NSE, but it does not work for attosecond and phase-modulated femtosecond laser pulses, where the spectral width of the pulse is of the order of the carrying frequency. In such cases, it is more convenient to use the general nonlinear amplitude equation (NAE). During the propagation of ultra-short pulses in optical fibers, the effects of the third-order linear dispersion and dispersion of nonlinearity become significant and have to be taken into account. We expanded the NAE by including these two effects. In this paper, we present an analytical study on the influence of third-order linear dispersion and dispersion of nonlinearity on the evolution of ultra-short optical pulses and on the possibility of dark soliton formation under such conditions in a medium with normal dispersion.
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