Solitary and periodic wave solutions of the generalized fourth‐order Boussinesq equation via He's variational methods

Yu‐Lan Ma, et al. (Mathematical Methods in the Applied Sciences, 2019,42(1)) make outstanding contributions for the soliton solutions of the generalized fourth‐order Boussinesq equation, which is used to describe the wave motion in fluid mechanics. But the periodic wave solution is not reported. So...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2021-05, Vol.44 (7), p.5617-5625
Main Authors: Wang, Kang‐Jia, Wang, Guo‐Dong
Format: Article
Language:English
Subjects:
Boussinesq equations
Computational fluid dynamics
Fluid mechanics
generalized fourth‐order Boussinesq equation
He's variational methods
semi‐inverse method
Solitary waves
Variational methods
variational principle
Waves
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Summary:Yu‐Lan Ma, et al. (Mathematical Methods in the Applied Sciences, 2019,42(1)) make outstanding contributions for the soliton solutions of the generalized fourth‐order Boussinesq equation, which is used to describe the wave motion in fluid mechanics. But the periodic wave solution is not reported. So in this paper, He's variational methods are employed to find the solitary and periodic wave solutions of the generalized fourth‐order Boussinesq equation. The greatest advantage of the variational method is that it can reduce the order of the research equation, make the equation more simple, and obtain the optimal solution. Finally, the numerical results are shown in the form of a graph to prove the applicability and effectiveness of the method. The results reveal that variational method is simple and straightforward and can avoid the tedious calculation process, which is expected to shed a light to the new research frontiers of solitary wave theory.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7135