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

Esen H., Ozdemir N., Seçer A., Bayram M.

Journal of Ocean Engineering and Science, vol.8, no.2, pp.124-132, 2023 (Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1016/j.joes.2021.12.006
  • Journal Name: Journal of Ocean Engineering and Science
  • Journal Indexes: Scopus
  • Page Numbers: pp.124-132
  • Keywords: Fourth-order equations, Riccati-Bernoulli sub -ODE method, Traveling wave solution, B?cklund transformation
  • Istanbul Gelisim University Affiliated: Yes


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.