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New non-traveling wave solutions for the (2+1)-dimensional variable coefficients Date-Jimbo-Kashiwara-Miwa equation

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  • Xu, Yuanqing
  • Zheng, Xiaoxiao
  • Xin, Jie

Abstract

In the paper, we mainly study the (2+1)-dimensional variable coefficients Date-Jimbo-Kashiwara-Miwa equation (VC-DJKM equation) by combining the extended homoclinic test approach and the generalized variable separation method. Applying this thought and with the aid of symbolic computation, we present thirty six kinds of new exact non-traveling wave solutions of the (2+1)-dimensional VC-DJKM equation including kink-like solution, singular solitary wave-like solution, periodic solitary wave-like solution, kinky breather wave-like solution, and so on. These results all have a like-parabolic tail which reveals the complex structure of solution and maybe give a prediction of physical phenomenon. The generalized variable separation method greatly enriches the types and structures of solutions. Moreover, when some functions in the generalized variable separation form take 0 or 1, it will degenerate into the variable separation form of multiplication or addition. As the special case of VC-DJKM equation, the corresponding results of the (2+1)-dimensional DJKM equation with constant coefficients are also given.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010158
    DOI: 10.1016/j.chaos.2021.111661
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    References listed on IDEAS

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    1. Shuxin Yang & Zhao Zhang & Biao Li, 2020. "Soliton Molecules and Some Novel Types of Hybrid Solutions to (2 + 1)-Dimensional Variable-Coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada Equation," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-9, January.
    2. Ma, Wen-Xiu, 2021. "N-soliton solution and the Hirota condition of a (2+1)-dimensional combined equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 270-279.
    3. 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.
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    Cited by:

    1. 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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