A novel scheme for SMCH equation with two different approaches

AKBULUT A., Islam S. M. R., Arafat S. M. Y., TAŞCAN F.

COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, vol.11, no.2, pp.263-280, 2023 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.22034/cmde.2022.50363.2093
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.263-280
  • Keywords: SMCH equation, The improved F-expansion method, The unified method, Symbolic computation, Exact solution, Solitary wave, WAVE SOLUTIONS, CAMASSA, SOLITONS
  • Eskisehir Osmangazi University Affiliated: Yes


In this study, the unified and improved F-expansion methods are applied to derive exact traveling wave solutions of the simplified modified Camassa-Holm (SMCH) equation. The current methods can calculate all branches of solutions at the same time, even if several solutions are quite near and therefore impossible to identify via numerical methods. All obtained solutions are given by hyperbolic, trigonometric, and rational function solutions which obtained solutions are useful for real-life problems in fluid dynamics, optical fibers, plasma physics and so on. The two-dimensional (2D) and three-dimensional (3D) graphs of the obtained solutions are plotted. Finally, we can state that these strategies are extremely successful, dependable, and simple. These ideas might potentially be applied to many nonlinear evolution models in mathematics and physics.