IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v162y2022ics0960077922006245.html
   My bibliography  Save this article

Lie symmetry reductions and generalized exact solutions of Date–Jimbo–Kashiwara–Miwa equation

Author

Listed:
  • Tanwar, Dig Vijay

Abstract

The propagation of nonlinear waves with nonuniform velocities is described by nonlinear evolution equations and their solutions involving arbitrary functions. When a nonlinear evolution equation is integrated, it reveals the several existing features of natural phenomena with continuous and fluctuating background. The Date–Jimbo–Kashiwara–Miwa equation is long water wave equation, which describes the propagation of nonlinear and weakly dispersive waves in inhomogeneous media. This work aims to extend the previous results and derive symmetry reductions of Date–Jimbo–Kashiwara–Miwa equation via Lie symmetry method. The infinitesimals involving four arbitrary functions are constructed by preserving invariance property of Lie groups under one parameter transformations. Then, the first symmetry reduction of test equation is determined using symmetry variables. The commutative and adjoint relations of four dimensional subalgebra are presented for reduced equation. Thereafter, the repeated utilization of Lie symmetry method results into the ordinary differential equations. These determining ODEs are solved under numeric constraints and provide exact solutions. The derived solutions retain all the four arbitrary functions appeared in infinitesimals and several arbitrary constants. Due to existing arbitrary functions, these solutions are generalized than previous established results. The deductions of previous results (Wang et al., 2014; Ali et al., 2021; Chauhan et al., 2020; Kumar and Kumar, 2020; Tanwar and Kumar, 2021; Kumar and Manju, 2022) show the novelty and significance of these solutions. Moreover, the derived results are expanded systematically with numerical simulation to analyze their physical significance and thus doubly soliton, multisoliton, line soliton, bell shape, parabolic nature are discussed.

Suggested Citation

  • Tanwar, Dig Vijay, 2022. "Lie symmetry reductions and generalized exact solutions of Date–Jimbo–Kashiwara–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
  • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006245
    DOI: 10.1016/j.chaos.2022.112414
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922006245
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2022.112414?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. Liu, Fei-Yan & Gao, Yi-Tian & Yu, Xin & Ding, Cui-Cui & Deng, Gao-Fu & Jia, Ting-Ting, 2021. "Painlevé analysis, Lie group analysis and soliton-cnoidal, resonant, hyperbolic function and rational solutions for the modified Korteweg-de Vries-Calogero-Bogoyavlenskii-Schiff equation in fluid mech," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Zhang, Yi, 2019. "Lie symmetry and invariants for a generalized Birkhoffian system on time scales," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 306-312.
    3. Sahadevan, R. & Prakash, P., 2017. "On Lie symmetry analysis and invariant subspace methods of coupled time fractional partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 107-120.
    4. Kumar, Raj & Kumar, Avneesh, 2022. "Dynamical behavior of similarity solutions of CKOEs with conservation law," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    5. Du, Xia-Xia & Tian, Bo & Qu, Qi-Xing & Yuan, Yu-Qiang & Zhao, Xue-Hui, 2020. "Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    6. Sadat, R. & Saleh, R. & Kassem, M. & Mousa, Mohamed M., 2020. "Investigation of Lie symmetry and new solutions for highly dimensional non-elastic and elastic interactions between internal waves," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    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. Rosa, M. & Gandarias, M.L. & Niño-López, A. & Chulián, S., 2023. "Exact solutions through symmetry reductions for a high-grade brain tumor model with response to hypoxia," Chaos, Solitons & Fractals, Elsevier, vol. 171(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. Stanislav Yu. Lukashchuk, 2022. "On the Property of Linear Autonomy for Symmetries of Fractional Differential Equations and Systems," Mathematics, MDPI, vol. 10(13), pages 1-17, July.
    2. Zhai, Yunyun & Ji, Ting & Geng, Xianguo, 2021. "Coupled derivative nonlinear Schrödinger III equation: Darboux transformation and higher-order rogue waves in a two-mode nonlinear fiber," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    3. Shahu, Chiranjeev K. & Dwivedi, Sharad & Dubey, Shruti, 2022. "Curved domain walls in the ferromagnetic nanostructures with Rashba and nonlinear dissipative effects," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    4. Nass, Aminu M., 2019. "Lie symmetry analysis and exact solutions of fractional ordinary differential equations with neutral delay," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 370-380.
    5. Singh, Sudhir & Sakkaravarthi, K. & Murugesan, K., 2022. "Localized nonlinear waves on spatio-temporally controllable backgrounds for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq model in water waves," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    6. 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).
    7. Hashemi, M.S., 2021. "A novel approach to find exact solutions of fractional evolution equations with non-singular kernel derivative," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Xie, Yingying & Li, Lingfei, 2022. "Multiple-order breathers for a generalized (3+1)-dimensional Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation near the offshore structure," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 19-31.
    9. Zhang, Yi & Jia, Yun-Die, 2023. "Generalization of Mei symmetry approach to fractional Birkhoffian mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    10. Jin, Shi-Xin & Chen, Xiang-Wei & Li, Yan-Min, 2024. "Approximate Noether theorem and its inverse for nonlinear dynamical systems with approximate nonstandard Lagrangian," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    11. Chen, Su-Su & Tian, Bo & Qu, Qi-Xing & Li, He & Sun, Yan & Du, Xia-Xia, 2021. "Alfvén solitons and generalized Darboux transformation for a variable-coefficient derivative nonlinear Schrödinger equation in an inhomogeneous plasma," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    12. Wang, Pan & Ma, Tian-Ping & Qi, Feng-Hua, 2021. "Analytical solutions for the coupled Hirota equations in the firebringent fiber," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    13. Chaudry Masood Khalique & Karabo Plaatjie, 2021. "Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation," Mathematics, MDPI, vol. 9(12), pages 1-17, June.
    14. 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).
    15. Zhang, Yi, 2019. "Lie symmetry and invariants for a generalized Birkhoffian system on time scales," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 306-312.
    16. Ávalos-Ruiz, L.F. & Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Romero-Ugalde, H.M., 2018. "FPGA implementation and control of chaotic systems involving the variable-order fractional operator with Mittag–Leffler law," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 177-189.
    17. Bakıcıerler, Gizel & Alfaqeih, Suliman & Mısırlı, Emine, 2021. "Analytic solutions of a (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    18. Liu, Yaqing & Peng, Linyu, 2023. "Some novel physical structures of a (2+1)-dimensional variable-coefficient Korteweg–de Vries system," Chaos, Solitons & Fractals, Elsevier, vol. 171(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:chsofr:v:162:y:2022:i:c:s0960077922006245. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.