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Multi-Soliton, Soliton–Cnoidal, and Lump Wave Solutions for the Supersymmetric Boussinesq Equation

Author

Listed:
  • Peng-Fei Wei

    (Department of Physics, Shaoxing University, Shaoxing 312000, China)

  • Hao-Bo Zhang

    (Department of Physics, Shaoxing University, Shaoxing 312000, China)

  • Ye Liu

    (Department of Physics, Shaoxing University, Shaoxing 312000, China)

  • Si-Yu Lin

    (Department of Physics, Shaoxing University, Shaoxing 312000, China)

  • Rui-Yu Chen

    (Department of Physics, Shaoxing University, Shaoxing 312000, China)

  • Zi-Yi Xu

    (Department of Physics, Shaoxing University, Shaoxing 312000, China)

  • Wan-Li Wang

    (Department of Mathematics, Zhejiang University of Technology, Hangzhou 310014, China)

  • Bo Ren

    (Department of Mathematics, Zhejiang University of Technology, Hangzhou 310014, China)

Abstract

Based on the bosonization approach, the supersymmetric Boussinesq equation is converted into a coupled bosonic system. The symmetry group and the commutation relations of the corresponding bosonic system are determined through the Lie point symmetry theory. The group invariant solutions of the coupled bosonic system are analyzed by the symmetry reduction technique. Special traveling wave solutions are generated by using the mapping and deformation method. Some novel solutions, such as multi-soliton, soliton–cnoidal interaction solutions, and lump waves, are given by utilizing the Hirota bilinear and the consistent tanh expansion methods. The methods in this paper can be effectively expanded to study rich localized waves for other supersymmetric systems.

Suggested Citation

  • Peng-Fei Wei & Hao-Bo Zhang & Ye Liu & Si-Yu Lin & Rui-Yu Chen & Zi-Yi Xu & Wan-Li Wang & Bo Ren, 2024. "Multi-Soliton, Soliton–Cnoidal, and Lump Wave Solutions for the Supersymmetric Boussinesq Equation," Mathematics, MDPI, vol. 12(13), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2002-:d:1424552
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    References listed on IDEAS

    as
    1. Wei, Peng-Fei & Long, Chun-Xiao & Zhu, Chen & Zhou, Yi-Ting & Yu, Hui-Zhen & Ren, Bo, 2022. "Soliton molecules, multi-breathers and hybrid solutions in (2+1)-dimensional Korteweg-de Vries-Sawada-Kotera-Ramani equation," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
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