The (3+1)-dimensional Boussinesq equation: Novel multi-wave solutions

The Boussinesq equation is a partial differential equation that describes the behavior of waves in shallow water. In this paper, we address some new dynamical behaviors to the (3+1)-dimensional Boussinesq equation, which are not constructed beforehand. Various solutions namely: multi-soliton, multi-...

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Bibliographic Details
Published in:Results in physics 2023-10, Vol.53, p.106965, Article 106965
Main Author: Ismael, Hajar Farhan
Format: Article
Language:English
Subjects:
(3+1)-dimensional Boussinesq equation
Hirota direct method
Long-wave method
M-lump
Mixed wave
Soliton
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Summary:The Boussinesq equation is a partial differential equation that describes the behavior of waves in shallow water. In this paper, we address some new dynamical behaviors to the (3+1)-dimensional Boussinesq equation, which are not constructed beforehand. Various solutions namely: multi-soliton, multi-M-lump, and the hybrid soliton solutions are reported. New explored features of equation are presented graphically to better analyze the gained solutions. For different period of time multi-soliton, multi-lump solutions are plotted. The results have important applications in oceanography, geophysics, fluid dynamics, and also used to study the behavior of waves in complex three-dimensional domains, particularly in situations where the nonlinear effects are strong. •The new (3+1)-dimensional Boussinesq equation is studied.•Multi-soliton and multiple M-lump waves are constructed.•Hybrid soliton waves are explored.•Extreme values and traveling equations for multi-M-lump waves are reported.•All reported solutions are novel and have not been reported beforehand.
ISSN:2211-3797
2211-3797
DOI:10.1016/j.rinp.2023.106965