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A comparative study of two fractional nonlinear optical model via modified \(\left( \frac{G^{\prime }}{G^2}\right)\)-expansion method

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Abstract

This article reveals the different types of optical solitons of non-linear coupled Riemann wave equation and Wazwaz Kaur Boussinesq equation. We adopted a direct integration technique namely, modified \(\left( \frac{G^{\prime }}{G^2}\right)\)-expansion. Different sorts of soliton’s existence criteria are also presented here. The proposed technique provides the new travelling wave solutions with the aid of different types of derivatives such as beta derivative, M-Truncated derivative and Conformable derivative and also offers special kinds of solutions including rational, trigonometric and hyperbolic solutions. In this work, we compared and analysed solitary wave solutions obtained by using different types of fractional derivatives. The outcomes of the study are highly significant for modern communication network technology, optical fiber, ion-acoustic, magneto-sound waves in plasma, and stationary media, particularly in the propagation of tidal and tsunami waves.

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Acknowledgements

This work is partly supported by the National Natural Science Foundation of China (NSFC) under Grant No. 72293574, the Natural Science Foundation of Hunan Province under Grant No. 2022JJ30677, the National Key Research and Development Program of China under Grant No. 2022YFC3303303.

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Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Vehari Campus, Vehari, Pakistan

    Abdul Saboor, Asim Zafar & Muhammad Ashraf

  2. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, China

    Muhammad Shakeel & Xinge Liu

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  1. Abdul Saboor
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  2. Muhammad Shakeel
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  3. Xinge Liu
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  4. Asim Zafar
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Saboor, A., Shakeel, M., Liu, X. et al. A comparative study of two fractional nonlinear optical model via modified \(\left( \frac{G^{\prime }}{G^2}\right)\)-expansion method. Opt Quant Electron 56, 259 (2024). https://doi.org/10.1007/s11082-023-05824-3

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