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In this work, we realised the soliton solutions of nonlinear Schrödinger equation (NLSE) that arise from optical fibers, we considered the modified Sardar sub-equation method (MSSEM) to find solitary solutions analytically. The stability of the retrieved soliton solutions realised from the NLSE are investigated. We demonstrate the soliton solutions that are stable and can last for a very long time without losing its form or energy under specific circumstances and those soliton solutions that are unstable. The MSSEM is a frequently employed technique in research for addressing specific mathematical modeling or physical phenomena problems. Its selection in this specific study might stem from its proven efficacy in handling the particular problem under investigation. The decision to utilize MSSEM could be driven by several considerations, including its precision, computationally efficient, effectiveness, greater accuracy and capability to manage intricate systems. Finally, our method offers greater flexibility in modeling various physical phenomena, which makes it particularly useful in applications in diverse fields such as quantum mechanics and nonlinear optics. The findings have ramifications for the architecture of optical fiber communications and offer significant new insights into the behavior of solitons in optical systems. The NLSE has proven to be an effective tool for understanding wave behavior in fiber optics. Its applications have helped engineers and scientists optimize the design of optical fibers and predict the behavior of various conditions. Moreover, our study provides insights into the fundamental properties of solitary solutions in the NLSEs and their practical implications in physical systems. [ABSTRACT FROM AUTHOR]

We study the interaction properties of optical soliton pulses propagating in a two-channel wavelength-division multiplexed strongly dispersion managed communication system. We analyze the effects of third order dispersion, Raman scattering and self-steepening using an ordinary differential equations model obtained by a variational method applied to the Generalized Nonlinear Schrödinger Equation. The validity of the model is assessed against the integration of the full nonlinear partial differential equations. The variational equations are initially solved for a single pulse in order to identify the launching parameters for each pulse in the first DM cell of the system. One pulse per wavelength is then injected in the transmission link. We then systematically study the evolution of multiplexed soliton trains and analyse the transmission system in terms of residual frequency shifts and interchannel interactions as the map strength is varied, focusing on the ratio of dissimilar peak powers in a broad range of dispersion difference values, concluding that the transmission characteristics improve by using specific values of unequal energies and considering higher-order correction terms. The work presented is an extension of previous analysis where isolated intra-channel two-pulse interactions had been addressed considering pulses with dissimilar energies. [ABSTRACT FROM AUTHOR]