Invariant subspaces, exact solutions and stability analysis of nonlinear water wave equations

•Nonlinear water wave equations describing specific nonlinear waves in oceans are studied.•The invariant subspace scheme is adopted to carry out this goal.•A series of exact solutions are derived.•The stability analysis is investigated in detail. The key purpose of the present research is to derive...

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Bibliographic Details
Published in:Journal of ocean engineering and science 2020-03, Vol.5 (1), p.35-40
Main Authors: Hosseini, K., Inc, M., Shafiee, M., Ilie, M., Shafaroody, A., Yusuf, A., Bayram, M.
Format: Article
Language:English
Subjects:
Exact solutions
Invariant subspace scheme
Nonlinear water wave equations
Stability analysis
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Summary:•Nonlinear water wave equations describing specific nonlinear waves in oceans are studied.•The invariant subspace scheme is adopted to carry out this goal.•A series of exact solutions are derived.•The stability analysis is investigated in detail. The key purpose of the present research is to derive the exact solutions of nonlinear water wave equations (NLWWEs) in oceans through the invariant subspace scheme (ISS). In this respect, the NLWWEs which describe specific nonlinear waves are converted to a number of systems of ordinary differential equations (ODEs) such that the resulting systems can be efficiently handled by computer algebra systems. As an accomplishment, the performance of the well-designed ISS in extracting a group of exact solutions is formally confirmed. In the end, the stability analysis for the NLWWE is investigated through the linear stability scheme.
ISSN:2468-0133
2468-0133
DOI:10.1016/j.joes.2019.07.004