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Breathers, Transformation Mechanisms and Their Molecular State of a (3+1)-Dimensional Generalized Yu–Toda–Sasa–Fukuyama Equation

Author

Listed:
  • Jian Zhang

    (School of Computer Science and Technology, China University of Mining and Technology, Xuzhou 221116, China)

  • Juan Yue

    (School of Mathematics, North University of China, Taiyuan 030051, China)

  • Zhonglong Zhao

    (School of Mathematics, North University of China, Taiyuan 030051, China)

  • Yufeng Zhang

    (School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China)

Abstract

A (3+1)-dimensional generalized Yu–Toda–Sasa–Fukuyama equation is considered systematically. N -soliton solutions are obtained using Hirota’s bilinear method. The employment of the complex conjugate condition of parameters of N -soliton solutions leads to the construction of breather solutions. Then, the lump solution is obtained with the aid of the long-wave limit method. Based on the transformation mechanism of nonlinear waves, a series of nonlinear localized waves can be transformed from breathers, which include the quasi-kink soliton, M-shaped kink soliton, oscillation M-shaped kink soliton, multi-peak kink soliton, and quasi-periodic wave by analyzing the characteristic lines. Furthermore, the molecular state of the transformed two-breather is studied using velocity resonance, which is divided into three aspects, namely the modes of non-, semi-, and full transformation. The analytical method discussed in this paper can be further applied to the investigation of other complex high-dimensional nonlinear integrable systems.

Suggested Citation

  • Jian Zhang & Juan Yue & Zhonglong Zhao & Yufeng Zhang, 2023. "Breathers, Transformation Mechanisms and Their Molecular State of a (3+1)-Dimensional Generalized Yu–Toda–Sasa–Fukuyama Equation," Mathematics, MDPI, vol. 11(7), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1755-:d:1117631
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    References listed on IDEAS

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    1. Ning, Tong-ke & Chen, Deng-yuan & Zhang, Da-jun, 2004. "The exact solutions for the nonisospectral AKNS hierarchy through the inverse scattering transform," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 339(3), pages 248-266.
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