Raising the number of channels causes numerous nonlinear phenomena. To explore nonlinear effects in photonic crystal fibers, brief pulses of 10 ns to 10 fs are used [1,2]. When pulse widths are shorter than one picosecond and peak power surpasses the threshold level, the influence of third-order dispersion must be considered. This article investigates dispersion and higher-order nonlinear effects, focusing on the propagation of pulses with widths ranging from tens to hundreds of femtoseconds. Partial differential equations can be solved using several mathematical approaches. These fall into two categories: finite difference techniques (FDM) and pseudo-spectral approaches. The split-step Fourier method (SSFM) is a popular pseudo-spectral technique for addressing pulse transmission in nonlinear dispersive materials. In this study, we employ a special variant of FDM known as the method of lines (MOL) [3]. We use this approach to solve NLSE and simulate Gaussian pulse propagation in optical fibers. As previously stated, we focused on the dispersion effects that cause pulse broadening in the temporal domain, as well as the higher-order nonlinear effects in the spectrum domain. We use this technique to mimic Gaussian pulse propagation in optical fibers and solve the NLSE. As previously stated, we have concentrated on the higher-order nonlinear effects in the spectrum domain as well as the dispersion effects that cause pulse broadening in the temporal domain [4]. Self-phase modulation and chromatic dispersion often cause a brief optical pulse's temporal and spectral structure to alter throughout its passage in a photonic crystal fiber. The fact that soliton solutions of the nonlinear wave equation are extremely stable is perhaps more astonishing than the feasibility of the balance between dispersion and nonlinearity.

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