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Rational Localized Waves and Their Absorb-Emit Interactions in the (2 + 1)-Dimensional Hirota–Satsuma–Ito Equation

Author

Listed:
  • Yuefeng Zhou

    (Department of Mathematics, Kunming University of Science and Technology, Kunming 650500, China)

  • Chuanjian Wang

    (Department of Mathematics, Kunming University of Science and Technology, Kunming 650500, China)

  • Xiaoxue Zhang

    (Department of Mathematics, Kunming University of Science and Technology, Kunming 650500, China)

Abstract

In this paper, we investigate the (2 + 1)-dimensional Hirota–Satsuma–Ito (HSI) shallow water wave model. By introducing a small perturbation parameter ϵ , an extended (2 + 1)-dimensional HSI equation is derived. Further, based on the Hirota bilinear form and the Hermitian quadratic form, we construct the rational localized wave solution and discuss its dynamical properties. It is shown that the oblique and skew characteristics of rational localized wave motion depend closely on the translation parameter ϵ . Finally, we discuss two different interactions between a rational localized wave and a line soliton through theoretic analysis and numerical simulation: one is an absorb-emit interaction, and the other one is an emit-absorb interaction. The results show that the delay effect between the encountering and parting time of two localized waves leads to two different kinds of interactions.

Suggested Citation

  • Yuefeng Zhou & Chuanjian Wang & Xiaoxue Zhang, 2020. "Rational Localized Waves and Their Absorb-Emit Interactions in the (2 + 1)-Dimensional Hirota–Satsuma–Ito Equation," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1807-:d:429156
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    Citations

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    Cited by:

    1. Ruijuan Li & Onur Alp İlhan & Jalil Manafian & Khaled H. Mahmoud & Mostafa Abotaleb & Ammar Kadi, 2022. "A Mathematical Study of the (3+1)-D Variable Coefficients Generalized Shallow Water Wave Equation with Its Application in the Interaction between the Lump and Soliton Solutions," Mathematics, MDPI, vol. 10(17), pages 1-17, August.
    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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