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On the Soliton Solutions for the Stochastic Konno–Oono System in Magnetic Field with the Presence of Noise

Author

Listed:
  • Tahira Sumbal Shaikh

    (Department of Mathematics, Lahore College for Women University, Lahore 54000, Pakistan)

  • Muhammad Zafarullah Baber

    (Department of Mathematics and Statistics, The University of Lahore, Lahore 54590, Pakistan)

  • Nauman Ahmed

    (Department of Mathematics and Statistics, The University of Lahore, Lahore 54590, Pakistan
    Department of Computer Science and Mathematics, Lebanese American University, Beirut P.O. Box 13-5053, Lebanon)

  • Naveed Shahid

    (Department of Mathematics and Statistics, The University of Lahore, Lahore 54590, Pakistan)

  • Ali Akgül

    (Department of Computer Science and Mathematics, Lebanese American University, Beirut P.O. Box 13-5053, Lebanon
    Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey
    Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, 99138 Nicosia, Turkey)

  • Manuel De la Sen

    (Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, 48940 Leioa, Spain)

Abstract

In this study, we consider the stochastic Konno–Oono system to investigate the soliton solutions under the multiplicative sense. The multiplicative noise is considered firstly in the Stratonovich sense and secondly in the It o ^ sense. Applications of the Konno–Oono system include current-fed strings interacting with an external magnetic field. The F-expansion method is used to find the different types of soliton solutions in the form of dark, singular, complex dark, combo, solitary, periodic, mixed periodic, and rational functions. These solutions are applicable in the magnetic field when we study it at the micro level. Additionally, the absolute, real, and imaginary physical representations in three dimensions and the corresponding contour plots of some solutions are drawn in the sense of noise by the different choices of parameters.

Suggested Citation

  • Tahira Sumbal Shaikh & Muhammad Zafarullah Baber & Nauman Ahmed & Naveed Shahid & Ali Akgül & Manuel De la Sen, 2023. "On the Soliton Solutions for the Stochastic Konno–Oono System in Magnetic Field with the Presence of Noise," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1472-:d:1100326
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    References listed on IDEAS

    as
    1. Iqbal, Muhammad S. & Seadawy, Aly R. & Baber, Muhammad Z. & Qasim, Muhammad, 2022. "Application of modified exponential rational function method to Jaulent–Miodek system leading to exact classical solutions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Mohammed, W.W. & El-Morshedy, M., 2021. "The influence of multiplicative noise on the stochastic exact solutions of the Nizhnik–Novikov–Veselov system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 192-202.
    3. Farah M. Al-Askar & Wael W. Mohammed & M. El-Morshedy & Saima Arshed, 2022. "The Analytical Solutions for Stochastic Fractional-Space Burgers’ Equation," Journal of Mathematics, Hindawi, vol. 2022, pages 1-8, March.
    4. Farah M. Al-Askar & Wael W. Mohammed & Qura tul Ain, 2022. "The Analytical Solutions of the Stochastic Fractional RKL Equation via Jacobi Elliptic Function Method," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-8, August.
    5. Saleh Alshammari & W. W. Mohammed & Sallieu K. Samura & S. Faleh & Amr Elsonbaty, 2022. "The Analytical Solutions for the Stochastic-Fractional Broer–Kaup Equations," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-9, August.
    6. M. E. Elbrolosy & A. A. Elmandouh & Abdellatif Ben Makhlouf, 2022. "Dynamical Behaviour of Conformable Time-Fractional Coupled Konno-Oono Equation in Magnetic Field," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-12, June.
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