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Traveling wave structures of some fourth-order nonlinear partial differential equations

Authors :
Handenur Esen
Neslihan Ozdemir
Aydin Secer
Mustafa Bayram
Mühendislik ve Doğa Bilimleri Fakültesi
Source :
Journal of Ocean Engineering and Science. 8:124-132
Publication Year :
2023
Publisher :
Elsevier BV, 2023.

Abstract

This study presents a large family of the traveling wave solutions to the two fourth-order nonlinear partial differential equations utilizing the Riccati-Bernoulli sub-ODE method. In this method, utilizing a traveling wave transformation with the aid of the Riccati-Bernoulli equation, the fourth-order equation can be transformed into a set of algebraic equations. Solving the set of algebraic equations, we acquire the novel exact solutions of the integrable fourth-order equations presented in this research paper. The physical interpretation of the nonlinear models are also detailed through the exact solutions, which demonstrate the effectiveness of the presented method.The Bäcklund transformation can produce an infinite sequence of solutions of the given two fourth-order nonlinear partial differential equations. Finally, 3D graphs of some derived solutions in this paper are depicted through suitable parameter values.

Details

ISSN :
24680133
Volume :
8
Database :
OpenAIRE
Journal :
Journal of Ocean Engineering and Science
Accession number :
edsair.doi.dedup.....f65baf6da3e13732fbfc9705f11b2d9c
Full Text :
https://doi.org/10.1016/j.joes.2021.12.006