IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v196y2022icp319-335.html
   My bibliography  Save this article

Symmetry reductions, generalized solutions and dynamics of wave profiles for the (2+1)-dimensional system of Broer–Kaup–Kupershmidt (BKK) equations

Author

Listed:
  • Kumar, Sachin
  • Dhiman, Shubham Kumar
  • Chauhan, Astha

Abstract

In this article, a (2+1)-dimensional system of Broer–Kaup–Kupershmidt (BKK) equations, which describes the non-linear, and long gravity waves in a dispersive system, is investigated by applying the method of Lie group of invariance. Applying the Lie group technique, the infinitesimals, vector fields, commutator table, and adjoint table are constructed for the BKK system. Furthermore, a one-dimensional optimal system of subalgebras is determined with the help of the adjoint transformation matrix; thereafter, the BKK system of equations is reduced into many systems of ordinary differential equations (ODEs) with respect to the similarity variables obtained through the symmetry reduction. These systems of ODEs are solved under some parametric constraints to obtain the exact closed form solutions. The obtained results are interpreted physically via graphical representation. Thus, dark–bright solitary waves, multi-peak mixed waves, breather type waves, periodic waves, multi-peakon solitons, and multi-solitons profiles of the obtained solutions are presented to make this research physically significant. A comparison is also presented between the solutions obtained in this article and the solutions reported by Kassem and Rashed in Kassem and Rashed (2019). The solutions obtained in this article are more general, and completely different in view of solutions obtained by Kassem and Rashed. The resulting solutions are found to be useful to understand the dynamics of BKK model and represent the authenticity as well as the effectiveness of the Lie group method. Therefore, the obtained solutions, and their dynamical wave structures are quite significant for understanding the propagation of the long gravity waves in a dispersive system. To obtain the infinitesimal generators and wave profiles of obtained solutions, symbolic computation is performed in the software package MAPLE and MATHEMATICA.

Suggested Citation

  • Kumar, Sachin & Dhiman, Shubham Kumar & Chauhan, Astha, 2022. "Symmetry reductions, generalized solutions and dynamics of wave profiles for the (2+1)-dimensional system of Broer–Kaup–Kupershmidt (BKK) equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 319-335.
    • Handle: RePEc:eee:matcom:v:196:y:2022:i:c:p:319-335
    DOI: 10.1016/j.matcom.2022.01.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422000374
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.01.024?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. Zheng, Chun-Long & Chen, Li-Qun, 2005. "Solitons with fission and fusion behaviors in a variable coefficient Broer–Kaup system," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1347-1351.
    2. Rashed, A.S., 2019. "Analysis of (3+1)-dimensional unsteady gas flow using optimal system of Lie symmetries," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 327-346.
    3. Kumar, Sachin & Kumar, Dharmendra & Kumar, Amit, 2021. "Lie symmetry analysis for obtaining the abundant exact solutions, optimal system and dynamics of solitons for a higher-dimensional Fokas equation," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Mohammadizadeh, Fatemeh & Rashidi, Saeede & Hejazi, S. Reza, 2021. "Space–time fractional Klein-Gordon equation: Symmetry analysis, conservation laws and numerical approximations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 476-497.
    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. El-Ganaini, Shoukry & Kumar, Sachin, 2023. "Symbolic computation to construct new soliton solutions and dynamical behaviors of various wave structures for two different extended and generalized nonlinear Schrödinger equations using the new impr," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 28-56.

    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. Kumar, Sachin & Kumar, Amit, 2022. "Dynamical behaviors and abundant optical soliton solutions of the cold bosonic atoms in a zig-zag optical lattice model using two integral schemes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 254-274.
    2. Geng, Tao & Shan, Wen-Rui & Lü, Xing & Cai, Ke-Jie & Zhang, Cheng & Tian, Bo, 2009. "New solitary solutions and non-elastic interactions of the (2+1)-dimensional variable-coefficient Broer–Kaup system with symbolic computation," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2230-2235.
    3. Melike Kaplan & Arzu Akbulut & Rubayyi T. Alqahtani, 2023. "New Solitary Wave Patterns of the Fokas System in Fiber Optics," Mathematics, MDPI, vol. 11(8), pages 1-11, April.
    4. Bashir, Azhar & Seadawy, Aly R. & Ahmed, Sarfaraz & Rizvi, Syed T.R., 2022. "The Weierstrass and Jacobi elliptic solutions along with multiwave, homoclinic breather, kink-periodic-cross rational and other solitary wave solutions to Fornberg Whitham equation," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    5. Aly R. Seadawy & Hanadi Zahed & Syed T. R. Rizvi, 2022. "Diverse Forms of Breathers and Rogue Wave Solutions for the Complex Cubic Quintic Ginzburg Landau Equation with Intrapulse Raman Scattering," Mathematics, MDPI, vol. 10(11), pages 1-22, May.
    6. Seadawy, Aly R. & Rizvi, Syed T.R. & Ahmed, Sarfaraz, 2022. "Multiple lump, generalized breathers, Akhmediev breather, manifold periodic and rogue wave solutions for generalized Fitzhugh-Nagumo equation: Applications in nuclear reactor theory," Chaos, Solitons & Fractals, Elsevier, vol. 161(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:matcom:v:196:y:2022:i:c:p:319-335. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.