TY - JOUR
T1 - Construction of bilinear Bäcklund transformation and complexitons for a newer form of Boussinesq equation describing shallow water waves
AU - Javed, Faisal
AU - Vivas-Cortez, Miguel
AU - Zil-E-Huma, null
AU - Raza, Nauman
AU - Alqarni, M.S.
N1 - Publisher Copyright:
© 2024 The Author(s)
PY - 2024/9
Y1 - 2024/9
N2 - This research investigates the characteristics and attributes of a new (3+ 1)-dimensional Boussinesq equation that describes shallow water waves in higher dimensions. By utilizing the Hirota bilinear representation, a bilinear Bäcklund transformation is provided for the proposed model to get soliton solutions. Then, the extended transform rational function method is applied to calculate the complexitons type solutions. The results demonstrate various exact solutions with different structures, including periodic, singular, and bright solitons. Comprehensive graphical representations in 2D, 3D, and density plots are provided to highlight the physical properties of these solutions. Our approach is distinguished by the unique nature of the problem and the use of previously untested methods in this context, leading to many new and original optical soliton solutions. These results highlight the effectiveness of the proposed method in tackling nonlinear problems in engineering and the natural sciences, exceeding previous work found in the literature.
AB - This research investigates the characteristics and attributes of a new (3+ 1)-dimensional Boussinesq equation that describes shallow water waves in higher dimensions. By utilizing the Hirota bilinear representation, a bilinear Bäcklund transformation is provided for the proposed model to get soliton solutions. Then, the extended transform rational function method is applied to calculate the complexitons type solutions. The results demonstrate various exact solutions with different structures, including periodic, singular, and bright solitons. Comprehensive graphical representations in 2D, 3D, and density plots are provided to highlight the physical properties of these solutions. Our approach is distinguished by the unique nature of the problem and the use of previously untested methods in this context, leading to many new and original optical soliton solutions. These results highlight the effectiveness of the proposed method in tackling nonlinear problems in engineering and the natural sciences, exceeding previous work found in the literature.
KW - Bäcklund transformation
KW - Complexitons
KW - Extended transformed rational function method
KW - Soliton solution
UR - https://doi.org/10.1016/j.rinp.2024.107903
UR - http://www.scopus.com/inward/record.url?scp=85200547932&partnerID=8YFLogxK
U2 - 10.1016/j.rinp.2024.107903
DO - 10.1016/j.rinp.2024.107903
M3 - Article
SN - 2211-3797
VL - 64
JO - Results in Physics
JF - Results in Physics
M1 - 107903
ER -