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New solitary wave solutions of space-time fractional dynamical models

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Abstract

In this article, new traveling wave solutions are retrieved for two space-time fractional models: the resonant nonlinear Schrödinger equation and the Biswas–Milovic equation which illustrates the dynamics of optical soliton promulgation in optical fibers, both featuring Kerr law nonlinearity. These equations are explored via an efficient method namely, the extended simple equation method. The fractional derivative is used in the conformable sense to accomplish this analysis. The extracted solutions show dark, periodic, singular, and singular-periodic solitons behaviors, which are depicted graphically by using line, surface, and contour plots. The reported solutions are unique and novel. The proposed method distinguishes itself by its simplicity, reliability, and ability to generate novel soliton solutions for nonlinear Schrödinger equations within the realm of mathematical physics.

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Funding

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through large group Research Project under Grant Number RGP2/222/44.

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Authors and Affiliations

  1. Division of Science and Technology, Department of Mathematics, University of Education, Lahore, Pakistan

    Wardat us Salam & Tehseen Fatima

  2. Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Azizah Hassan Alrajhi

  3. Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan

    Nauman Raza

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  1. Wardat us Salam
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  2. Azizah Hassan Alrajhi
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  3. Tehseen Fatima
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  4. Nauman Raza
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All authors contributed in preparation, design and study the problem. All authors read and approved the final manuscript.

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Correspondence to Nauman Raza.

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us Salam, W., Alrajhi, A.H., Fatima, T. et al. New solitary wave solutions of space-time fractional dynamical models. Opt Quant Electron 56, 1028 (2024). https://doi.org/10.1007/s11082-024-06935-1

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