IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i6p1472-d1100326.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/6/1472/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/6/1472/
    Download Restriction: no
    ---><---

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Muhammad Zafarullah Baber & Nauman Ahmed & Muhammad Waqas Yasin & Muhammad Sajid Iqbal & Ali Akgül & Alicia Cordero & Juan R. Torregrosa, 2024. "Comparisons of Numerical and Solitary Wave Solutions for the Stochastic Reaction–Diffusion Biofilm Model including Quorum Sensing," Mathematics, MDPI, vol. 12(9), pages 1-30, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & M. El-Morshedy, 2023. "Solitary Wave Solutions of the Fractional-Stochastic Quantum Zakharov–Kuznetsov Equation Arises in Quantum Magneto Plasma," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    2. Faridi, Waqas Ali & Wazwaz, Abdul-Majid & Mostafa, Almetwally M. & Myrzakulov, Ratbay & Umurzakhova, Zhanar, 2024. "The Lie point symmetry criteria and formation of exact analytical solutions for Kairat-II equation: Paul-Painlevé approach," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. AlQahtani, Salman A. & Alngar, Mohamed E.M. & Shohib, Reham M.A. & Pathak, Pranavkumar, 2023. "Highly dispersive embedded solitons with quadratic χ(2) and cubic χ(3) non-linear susceptibilities having multiplicative white noise via Itô calculus," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    4. Zainab, Iqra & Akram, Ghazala, 2023. "Effect of β-derivative on time fractional Jaulent–Miodek system under modified auxiliary equation method and exp(−g(Ω))-expansion method," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    5. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & M. El-Morshedy, 2023. "On the Dynamics of Solitary Waves to a (3+1)-Dimensional Stochastic Boiti–Leon–Manna–Pempinelli Model in Incompressible Fluid," Mathematics, MDPI, vol. 11(10), pages 1-9, May.
    6. Wael W. Mohammed & Farah M. Al-Askar & Clemente Cesarano & Elkhateeb S. Aly, 2023. "The Soliton Solutions of the Stochastic Shallow Water Wave Equations in the Sense of Beta-Derivative," Mathematics, MDPI, vol. 11(6), pages 1-11, March.
    7. Zayed, Elsayed M.E. & Alngar, Mohamed E.M. & Shohib, Reham M.A. & Biswas, Anjan & Yıldırım, Yakup & Moraru, Luminita & Mereuta, Elena & Alshehri, Hashim M., 2022. "Embedded solitons with χ(2) and χ(3) nonlinear susceptibilities having multiplicative white noise via Itô Calculus," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    8. Zayed, Elsayed M.E. & Alngar, Mohamed E.M. & Shohib, Reham M.A., 2023. "Cubic-quartic embedded solitons with χ(2) and χ(3) nonlinear susceptibilities having multiplicative white noise via Itô calculus," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    9. Muhammad Zafarullah Baber & Nauman Ahmed & Muhammad Waqas Yasin & Muhammad Sajid Iqbal & Ali Akgül & Alicia Cordero & Juan R. Torregrosa, 2024. "Comparisons of Numerical and Solitary Wave Solutions for the Stochastic Reaction–Diffusion Biofilm Model including Quorum Sensing," Mathematics, MDPI, vol. 12(9), pages 1-30, April.
    10. Elsayed M. E. Zayed & Mohamed E. M. Alngar & Reham M. A. Shohib, 2022. "Dispersive Optical Solitons to Stochastic Resonant NLSE with Both Spatio-Temporal and Inter-Modal Dispersions Having Multiplicative White Noise," Mathematics, MDPI, vol. 10(17), pages 1-18, September.
    11. Anwar Aldhafeeri & Muneerah Al Nuwairan, 2023. "Bifurcation of Some Novel Wave Solutions for Modified Nonlinear Schrödinger Equation with Time M-Fractional Derivative," Mathematics, MDPI, vol. 11(5), pages 1-14, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1472-:d:1100326. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.