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Optical Solutions of the Date–Jimbo–Kashiwara–Miwa Equation via the Extended Direct Algebraic Method

Author

Listed:
  • Ghazala Akram
  • Naila Sajid
  • Muhammad Abbas
  • Y. S. Hamed
  • Khadijah M. Abualnaja
  • Ahmet Ocak Akdemir

Abstract

In this study, the solutions of 2+1-dimensional nonlinear Date–Jimbo–Kashiwara–Miwa (DJKM) equation are characterized, which can be used in mathematical physics to model water waves with low surface tension and long wavelengths. The integration scheme, namely, the extended direct algebraic method, is used to extract complex trigonometric, rational and hyperbolic functions. The complex-valued solutions represent traveling waves in different structures, such as bell-, V-, and W-shaped multiwaves. The results obtained in this article are novel and more general than those contained in the literature (Wang et al., 2014, Yuan et al., 2017, Pu and Hu 2019, Singh and Gupta 2018). Furthermore, the mechanical features and dynamical characteristics of the obtained solutions are demonstrated by three-dimensional graphics.

Suggested Citation

  • Ghazala Akram & Naila Sajid & Muhammad Abbas & Y. S. Hamed & Khadijah M. Abualnaja & Ahmet Ocak Akdemir, 2021. "Optical Solutions of the Date–Jimbo–Kashiwara–Miwa Equation via the Extended Direct Algebraic Method," Journal of Mathematics, Hindawi, vol. 2021, pages 1-18, July.
    • Handle: RePEc:hin:jjmath:5591016
    DOI: 10.1155/2021/5591016
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    Cited by:

    1. Xu, Yuanqing & Zheng, Xiaoxiao & Xin, Jie, 2022. "New non-traveling wave solutions for the (2+1)-dimensional variable coefficients Date-Jimbo-Kashiwara-Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Singh, Shailendra & Saha Ray, S., 2023. "Integrability and new periodic, kink-antikink and complex optical soliton solutions of (3+1)-dimensional variable coefficient DJKM equation for the propagation of nonlinear dispersive waves in inhomog," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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