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Study of soliton solutions with different wave formations to model of nonlinear Schrödinger equation with mixed derivative and applications

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Abstract

In this paper, we investigate the impact of the integrability criterion on mixed-derivative nonlinear Schrödinger equations, specifically focusing on the Rangwala-Rao \((\mathcal {R}\mathcal {R})\) 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 \((\mathcal {R}\mathcal {R})\) equation. The study of the Rangwala-Rao \((\mathcal {R}\mathcal {R})\) 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.

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  1. Department of mathematics, Faculty of Science, University of Gujrat, Gujrat, Pakistan

    Jamshad Ahmad & Sobia Rani

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  1. Jamshad Ahmad
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  2. Sobia Rani
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J.A.: Resources, supervision, validation, acquisition. S.R.: Conceptualization, methodology, writing—original draft, formal analysis, validation. software.

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Correspondence to Jamshad Ahmad.

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Ahmad, J., Rani, S. Study of soliton solutions with different wave formations to model of nonlinear Schrödinger equation with mixed derivative and applications. Opt Quant Electron 55, 1195 (2023). https://doi.org/10.1007/s11082-023-05477-2

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