IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v440y2023ics0096300322007317.html
   My bibliography  Save this article

Nonclassical potential symmetry analysis and exact solutions for a thin film model of a perfectly soluble anti-surfactant solution

Author

Listed:
  • Sil, Subhankar
  • Raja Sekhar, T.

Abstract

In this article, we construct exact solutions to a quasilinear system of hyperbolic partial differential equations which governs the dynamics of a thin film of a perfectly soluble anti-surfactant solution. The symmetry analysis for this system is performed first time in the literature to the best of our knowledge. In fact, we present a detailed and comprehensive study of symmetry analysis for the governing system and compute classical symmetries, nonclassical symmetries, nonlocal symmetries and nonclassical potential symmetries. Nonclassical potential symmetries appear to be very much useful in terms of obtaining several new hidden solutions of the system that can not be established by using classical symmetry reductions, nonclassical symmetry method, or potential symmetry analysis. By using the direct multipliers we demonstrate several conserved quantities of the governing system those yield associated nonlocally related potential systems to the given system. Further, we prove that the given system admits a nonlocal symmetry that arises from the symmetry-based method and consequently we obtain a family of exact solutions. We analyze the physical interpretation of some of the obtained solutions which include various soliton type solutions such as kink type solitons, breather type solitons, multiple solitons, singular kink type solitons and etc. Lastly, as an application, we analyze the evolutionary property of characteristic shock, weak discontinuity and collision between them by using one of the obtained solutions.

Suggested Citation

  • Sil, Subhankar & Raja Sekhar, T., 2023. "Nonclassical potential symmetry analysis and exact solutions for a thin film model of a perfectly soluble anti-surfactant solution," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    • Handle: RePEc:eee:apmaco:v:440:y:2023:i:c:s0096300322007317
    DOI: 10.1016/j.amc.2022.127660
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322007317
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127660?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sil, Subhankar & Raja Sekhar, T. & Zeidan, Dia, 2020. "Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Satapathy, Purnima & Raja Sekhar, T., 2018. "Optimal system, invariant solutions and evolution of weak discontinuity for isentropic drift flux model," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 107-116.
    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. Mandal, Sougata & Sil, Subhankar & Ghosh, Sukhendu, 2024. "Lie symmetries and optimal classifications with certain modal approaches for the three-dimensional gas-dynamical equations," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

    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. Shagolshem, Sumanta & Bira, B. & Zeidan, D., 2023. "Optimal subalgebras and conservation laws with exact solutions for biological population model," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Karna, Ashutosh Kumar & Satapathy, Purnima, 2023. "Lie symmetry analysis for the Cargo–Leroux model with isentropic perturbation pressure equation of state," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    3. Manjit Singh & Shou-Fu Tian, 2023. "Lie symmetries, group classification and conserved quantities of dispersionless Manakov–Santini system in (2+1)-dimension," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(2), pages 312-329, June.
    4. Mandal, Sougata & Sil, Subhankar & Ghosh, Sukhendu, 2024. "Lie symmetries and optimal classifications with certain modal approaches for the three-dimensional gas-dynamical equations," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    5. Shagolshem, Sumanta & Bira, B. & Sil, Subhankar, 2022. "Conservation laws and some new exact solutions for traffic flow model via symmetry analysis," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    6. Shah, Sarswati & Singh, Randheer & Jena, Jasobanta, 2022. "Steepened wave in two-phase Chaplygin flows comprising a source term," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    7. Simon, S. Gimnitz & Bira, B. & Zeidan, Dia, 2023. "Optimal systems, series solutions and conservation laws for a time fractional cancer tumor model," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    8. Silambarasan, Rathinavel & Baskonus, Haci Mehmet & Vijay Anand, R. & Dinakaran, M. & Balusamy, Balamurugan & Gao, Wei, 2021. "Longitudinal strain waves propagating in an infinitely long cylindrical rod composed of generally incompressible materials and its Jacobi elliptic function solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 566-602.
    9. 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).
    10. K. Krishnakumar & A. Durga Devi & V. Srinivasan & P. G. L. Leach, 2023. "Optimal system, similarity solution and Painlevé test on generalized modified Camassa-Holm equation," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(2), pages 547-557, June.
    11. Sil, Subhankar & Raja Sekhar, T. & Zeidan, Dia, 2020. "Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

    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:eee:apmaco:v:440:y:2023:i:c:s0096300322007317. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.