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This paper represents a comprehensive exploration of mathematical modeling and analysis in the context of fiber communications, with a specific focus on optimizing performance and efficiency. Positioned at the vanguard of innovation within the field of nonlinear optics, this research stands as a pioneering effort, venturing into uncharted territory by comprehensively examining soliton solutions. We direct our inquiry to the cubic-quartic nonlinear Schrödinger equation model, specifically as applied to birefringent fibers exhibiting cubic-quintic-septic-nonic (CQSN) nonlinearity. This study delivers a distinctive and noteworthy contribution to the scientific landscape. Employing advanced mathematical techniques, notably the generalized auxiliary equation technique, we have derived a diverse array of soliton solutions for CQ optical solitons within birefringent fibers. These solutions encompass dark, bright, singular, combo-bright-dark, and combo-singular solitons. Through the lens of the CQSN nonlinear Schrödinger’s equation, our investigation delves into the dynamic behavior of the system and its implications for fiber communication. This manuscript encapsulates original and innovative research, illuminating the potential of mathematical methodologies to enhance the design and operation of fiber communication systems. It underscores the pioneering essence of our study, emphasizing the practical significance of our findings in advancing the field of nonlinear optics and its potential impact on real-world applications.

The ongoing research centers its attention on the Kerr nonlinear cascaded system, but this time in (2+1) dimensions. In this study, we employ the Φ6-model expansion approach to investigate the generation of bright, dark, and singular solitons in the cascaded system. Optical solitons are self-sustaining wave packets that can maintain their shape and propagate without dispersion. The cascaded system, governed by coupled NLSE, has wide-ranging applications in various fields such as waveguide dynamics, optical communications, nonlinear optics, ultrafast optics, nonlinear imaging, and photonic devices. After evaluating limitations of the modulus of ellipticity, Jacobi’s elliptic function yields soliton solutions.

This paper is about the retrieval of highly dispersive optical solitons for Sasa-Satsuma equation with differential group delay in presence of white noise. There are four integration schemes that make this retrieval possible. A full spectrum of optical solitons have been revealed from these schemes. The parametric restrictions for the existence of such solitons are also presented. The displayed surface plots support the analytical findings.

This paper recovers gap solitons from Bragg gratings of the concatenation model. The new mapping method recovers a full spectrum of optical solitons. The parameter constraints for the existence of such solitons are enumerated.

This article obtains the parameter dynamics of super-Gaussian and super-sech pulses for the perturbed nonlinear Schrödinger’s equation with quadratic-cubic and generalized quadratic-cubic forms of self-phase modulation structures. The implemented variational principle successfully recovers this dynamical system.

The current paper aims to explore the dynamics of optical solitons in the presence of multiplicative white noise within a DWDM topology. The utilization of Jacobi’s elliptic function and Itô Calculus has made it possible to retrieve the soliton solutions. The presence of white noise has an exclusive effect on the phase component of the solitons.