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Study of Stochastic–Fractional Drinfel’d–Sokolov–Wilson Equation for M-Shaped Rational, Homoclinic Breather, Periodic and Kink-Cross Rational Solutions

Author

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  • Shami A. M. Alsallami

    (Department of Mathematical Sciences, College of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia)

  • Syed T. R. Rizvi

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54840, Pakistan)

  • Aly R. Seadawy

    (Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah 41411, Saudi Arabia)

Abstract

We explore stochastic–fractional Drinfel’d–Sokolov–Wilson (SFDSW) equations for some wave solutions such as the cross-kink rational wave solution, periodic cross-rational wave solution and homoclinic breather wave solution. We also examine some M-shaped solutions such as the M-shaped rational solution, M-shaped rational solution with one and two kink waves. We also derive the M-shaped interaction with rogue and kink waves and the M-shaped interaction with periodic and kink waves. This model is used in mathematical physics, surface physics, plasma physics, population dynamics and applied sciences. Moreover, we also show our results graphically in different dimensions. We obtain these solutions under some constraint conditions.

Suggested Citation

  • Shami A. M. Alsallami & Syed T. R. Rizvi & Aly R. Seadawy, 2023. "Study of Stochastic–Fractional Drinfel’d–Sokolov–Wilson Equation for M-Shaped Rational, Homoclinic Breather, Periodic and Kink-Cross Rational Solutions," Mathematics, MDPI, vol. 11(6), pages 1-25, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1504-:d:1102019
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    References listed on IDEAS

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    4. Ruijuan Li & Onur Alp İlhan & Jalil Manafian & Khaled H. Mahmoud & Mostafa Abotaleb & Ammar Kadi, 2022. "A Mathematical Study of the (3+1)-D Variable Coefficients Generalized Shallow Water Wave Equation with Its Application in the Interaction between the Lump and Soliton Solutions," Mathematics, MDPI, vol. 10(17), pages 1-17, August.
    5. Rizvi, Syed T.R. & Seadawy, Aly R. & Farah, N. & Ahmad, S., 2022. "Application of Hirota operators for controlling soliton interactions for Bose-Einstien condensate and quintic derivative nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
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    Cited by:

    1. Syed T. R. Rizvi & Aly R. Seadawy & Shami A. M. Alsallami, 2023. "Grey-Black Optical Solitons, Homoclinic Breather, Combined Solitons via Chupin Liu’s Theorem for Improved Perturbed NLSE with Dual-Power Law Nonlinearity," Mathematics, MDPI, vol. 11(9), pages 1-19, April.

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