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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]

This paper builds exact optical solitons to the coupled of nonlinear equations which describes the pulse propagation in birefringent optical fibers with the effects of ellipticity angle and coupling coefficient. By adopting the new Sardar sub-ODE method, diverse optical solitons as W-shaped bright, dark optical solitons, trigonometric function and singular function solutions have been secured. To show out the warranty of the stability of the acquired results, we examine the effects of the ellipticity angle and coupling coefficient on modulation instability. It is noted beside of the linear and circular birefringence, for θ = 45 o , it is exhibited unstable zone where MI growth rate. To enroll the effects of the coupling coefficient on MI growth rate, we fixed a value of the ellipticity angle θ = 45 o . In Figs. 6 and 10, we acquired some new behavior of the MI gain compared to Houwe et al. (2021). These results show out stable/unstable zones compared to Ablowitz and Horikis (2017), Houwe et al. (2021). Moreover, these results will be helpful in nonlinear optical fibers to explain the communication over long distance and optical fibers design. [ABSTRACT FROM AUTHOR]