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Effects of integrability criterion on nonlinear Schrödinger equations with mixed derivatives: insights from the Rangwala–Rao equation

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Abstract

This study explores the impact of the integrability criterion on nonlinear Schrödinger (\(\mathcal {NLS}\)) equations with mixed derivatives, specifically focusing on the Rangwala–Rao (\({{\mathcal {R}}}{{\mathcal {R}}}\)) 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.

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Data Availibility Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

I greatly thank the journal stuff (Editors and Reviewers) for their support and help.

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Authors and Affiliations

  1. School of Medical Informatics and Engineering, Xuzhou Medical University, 209 Tongshan Road, Xuzhou, 221004, Jiangsu Province, People’s Republic of China

    Mostafa M. A. Khater

  2. Department of Basic Science, Obour High Institute for Engineering and Technology, 11828, Cairo, Egypt

    Mostafa M. A. Khater

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  1. Mostafa M. A. Khater
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Correspondence to Mostafa M. A. Khater.

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Khater, M.M.A. Effects of integrability criterion on nonlinear Schrödinger equations with mixed derivatives: insights from the Rangwala–Rao equation. Opt Quant Electron 55, 779 (2023). https://doi.org/10.1007/s11082-023-04993-5

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