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

Peng-Fei Wei, Hao-Bo Zhang, Ye Liu, Si-Yu Lin, Rui-Yu Chen, Zi-Yi Xu, Wan-Li Wang and Bo Ren ()
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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

Mathematics, 2024, vol. 12, issue 13, 1-10

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.

Keywords: supersymmetric Boussinesq equation; bosonization approach; Lie point symmetry theory; mapping and deformation method; consistent tanh expansion method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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