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Rational Solutions and Their Interaction Solutions of the ( )- Dimensional Jimbo-Miwa Equation

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  • Xiaomin Wang
  • Sudao Bilige
  • Jing Pang

Abstract

In this paper, we gave a form of rational solution and their interaction solution to a nonlinear evolution equation. The rational solution contained lump solution, general lump solution, high-order lump solution, lump-type solution, etc. Their interaction solution contained the classical interaction solution, such as the lump-kink solution and the lump-soliton solution. As the example, by using the generalized bilinear method and symbolic computation Maple, we obtained abundant high-order lump-type solutions and their interaction solutions between lumps and other function solutions under certain constraints of the ( )- dimensional Jimbo-Miwa equation. Via three-dimensional plots, contour plots and density plots with the help of Maple, the physical characteristics and structures of these waves are described very well. These solutions have greatly enriched the exact solutions of the ( )- dimensional Jimbo-Miwa equation on the existing literature.

Suggested Citation

  • Xiaomin Wang & Sudao Bilige & Jing Pang, 2020. "Rational Solutions and Their Interaction Solutions of the ( )- Dimensional Jimbo-Miwa Equation," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-18, April.
    • Handle: RePEc:hin:jnlamp:9260986
    DOI: 10.1155/2020/9260986
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    Cited by:

    1. Zhang, Run-Fa & Li, Ming-Chu & Albishari, Mohammed & Zheng, Fu-Chang & Lan, Zhong-Zhou, 2021. "Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada-like equation," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    2. Sudao Bilige & Leilei Cui & Xiaomin Wang, 2023. "Superposition Formulas and Evolution Behaviors of Multi-Solutions to the (3+1)-Dimensional Generalized Shallow Water Wave-like Equation," Mathematics, MDPI, vol. 11(8), pages 1-12, April.

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