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Exploring soliton solutions in nonlinear spatiotemporal fractional quantum mechanics equations: an analytical study

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Abstract

In this work, travelling wave solutions of a nonlinear system of fractional Schrödinger equations (FSEs) with conformable fractional derivatives are studied. We examine the fractional generalization of the Schrödinger equation, a topic of great importance in quantum physics, using the analytic approach known as the modified extended direct algebraic method. Our approach involves the use of a fractional complex transformation to produce nonlinear ordinary differential equations, which are then solved to reveal travelling wave solutions. The two- and three-dimensional graphs that provide visual representations of the system’s behaviour present a variety of wave profiles, including periodic, kink, anti-kink, shocks, lumps, and other soliton waves. The study sheds light on the dynamics of FSEs by revealing multiple families of travelling wave solutions and their complex relationships. These results provide insight into nonlinear fractional partial differential equations and a greater understanding of the dynamics of FSEs than previous attempts in the literature.

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Acknowledgements

We are grateful for the suggestions and comments provided by the four referees, which significantly improved the quality of the paper.

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang Normal University, 688 Yingbin Road, Jinhua, 321004, Zhejiang, People’s Republic of China

    Rashid Ali & Zhao Zhang

  2. Near East University, Operational Research Center in Healthcare, Nicosia, Turkey

    Hijaz Ahmad

  3. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

    Hijaz Ahmad

  4. Center for Applied Mathematics and Bioinformatics, Gulf University for Science and Technology, Mishref, Kuwait

    Hijaz Ahmad

  5. Department of Mathematics and Informatics, Azerbaijan University, Jeyhun Hajibeyli street, 71, AZ1007, Baku, Azerbaijan

    Hijaz Ahmad

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  1. Rashid Ali
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  2. Zhao Zhang
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Contributions

Conceptualization: RA. Data curation: ZZ. Formal analysis: RA. Validation: HA. Writing—original draft: RA. Writing—review editing: HA.

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Correspondence to Hijaz Ahmad.

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Ali, R., Zhang, Z. & Ahmad, H. Exploring soliton solutions in nonlinear spatiotemporal fractional quantum mechanics equations: an analytical study. Opt Quant Electron 56, 838 (2024). https://doi.org/10.1007/s11082-024-06370-2

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