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Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type

Author

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  • Abd-Allah Hyder

    (Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
    Department of Engineering Mathematics and Physics, Faculty of Engineering, Al-Azhar University, Cairo 11371, Egypt)

  • Ahmed H. Soliman

    (Department of Mathematics, Faculty of Sciences, Al-Azhar University, Assiut 71524, Egypt)

  • Clemente Cesarano

    (Section of Mathematics, Università Telematica Internazionale Uninettuno, 00186 Rome, Italy)

  • M. A. Barakat

    (Department of Mathematics, Faculty of Sciences, Al-Azhar University, Assiut 71524, Egypt
    Department of Computer Science, College of Al Wajh, University of Tabuk, Tabuk 71491, Saudi Arabia)

Abstract

This work is devoted to providing new kinds of deterministic and stochastic solutions of one of the famous nonlinear equations that depends on time, called the Schrödinger–Hirota equation. A new and straightforward methodology is offered to extract exact wave solutions of the stochastic nonlinear evolution equations (NEEs) with generalized differential conformable operators (GDCOs). This methodology combines the features of GDCOs, some instruments of white noise analysis, and the generalized Kudryashov scheme. To demonstrate the usefulness and validity of our methodology, we applied it to extract diversified exact wave solutions of the Schrödinger–Hirota equation, particularly in a Wick-type stochastic space and with GDCOs. These wave solutions can be turned into soliton and periodic wave solutions that play a main role in numerous fields of nonlinear physical sciences. Moreover, three-dimensional, contour, and two-dimensional graphical visualizations of some of the extracted solutions are exhibited with some elected functions and parameters. According to the results, our new approach demonstrates the impact of random and conformable factors on the solutions of the Schrödinger–Hirota equation. These findings can be applied to build new models in plasma physics, condensed matter physics, industrial studies, and optical fibers. Furthermore, to reinforce the importance of the acquired solutions, comparative aspects connected to some former works are presented for these types of solutions.

Suggested Citation

  • Abd-Allah Hyder & Ahmed H. Soliman & Clemente Cesarano & M. A. Barakat, 2021. "Solving Schrödinger–Hirota Equation in a Stochastic Environment and Utilizing Generalized Derivatives of the Conformable Type," Mathematics, MDPI, vol. 9(21), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2760-:d:668640
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    References listed on IDEAS

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    4. Saha Ray, S., 2020. "Dispersive optical solitons of time-fractional Schrödinger–Hirota equation in nonlinear optical fibers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    5. Ulutas, Esma, 2021. "Travelling wave and optical soliton solutions of the Wick-type stochastic NLSE with conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
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