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In this paper, we investigate the impact of the integrability criterion on mixed-derivative nonlinear Schrödinger equations, specifically focusing on the Rangwala-Rao (R R) equation introduced by A. Rangwala in 1990. Our objective is to enhance our understanding of the dispersion effect by examining innovative soliton wave solutions and their interactions. The tanh method is utilized to generate unique solitary wave solutions for the Rangwala-Rao (R R) equation. The study of the Rangwala-Rao (R R) holds significance as it has the potential to contribute to the development of more efficient optical fiber communication systems. The numerical solutions presented in this research illustrate the dynamic nature of optical fiber pulse propagation, underscoring the distinctiveness of this work compared to previous scholarly endeavors. The study obtained various soliton solutions, including rational, trigonometric, and hyperbolic functions. The results are presented in graphical form with appropriate parameter values to aid visualization. The originality of our computed outcomes, which represent novel achievements that surpass previously derived solutions, becomes evident when we compare our accomplishments with theirs. These newly examined results are innovative and novel, with the potential to significantly propel the realms of nonlinear optics and mathematical physics forward. This study proves that the computational method used is efficient, brief, and widely applicable, making it valuable to engineers who work with engineering models and dynamical models. [ABSTRACT FROM AUTHOR]

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 study explores the impact of the integrability criterion on nonlinear Schrödinger (NLS ) equations with mixed derivatives, specifically focusing on the Rangwala–Rao ( R R ) equation formulated by A. Rangwala in 1990. The objective of this investigation is to enhance our understanding of the dispersion effect by examining novel soliton wave solutions and their interactions. By doing so, we aim to gain insights into the behavior of the slowly changing envelope of the electric field and pulse propagation in optical fibers. To achieve this, we employ recent computational approaches, including the Sardar Sub-equation and modified rational methods, to identify distinctive solitary wave solutions for the analyzed model. The significance of studying the Rangwala–Rao equation lies in its potential contribution to the development of more efficient optical fiber communication systems. The presented numerical solutions in this paper showcase the dynamic nature of optical fiber pulse propagation, thereby highlighting the originality of this work compared to existing scholarly contributions. [ABSTRACT FROM AUTHOR]

The main focus of this research is to acquire innovatory solutions to the resonant fractional nonlinear Schrödinger equation (R-FNLSE) with quadratic cubic nonlinearity. This objective has been attained by applying two most reliable and efficient integrating techniques namely: the (G ′ G 2) -expansion technique and an equivalent form for the (exp (- ϕ (ξ))) -expansion technique. The beta derivative has been used for describing the fractional effects involved in the proposed model. The R-FNLSE plays an important role in the theory of fiber optic and telecommunication. The results received by employing the proposed analytical approaches have been classified as hyperbolic, rational and trigonometric solutions. On the basis of linear stability, the proposed model has been investigated for modulation instability. The dynamics of the extracted solution has also been tested by 3D plots and line plot. [ABSTRACT FROM AUTHOR]