Painlevé Analysis, Lie Symmetries and Abundant Wave Solutions for Family Fifth Order Kdv Equations

Authors

  • Ahmed Gaber Department of Mathematics, College of Science Al-Zulfi, Majmaah University, 11952, Suadi Arabia https://orcid.org/0009-0006-0948-3207
  • Doaa M. Mostafa Department of Mathematics, College of Science, Qassim University, P. O. Box 6644, Buraidah 51452, Saudi Arabia; Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt https://orcid.org/0000-0002-0888-8978

DOI:

https://doi.org/10.26713/cma.v15i3.2752

Keywords:

Painlevé analysis, Lie symmetries, (G′/G)-expansion method, Wave solutions, Fifth-order KdV equation

Abstract

In this paper, we study integrability, similarity reduction and obtaining abundant solutions for the family fifth-order KdV equation. This equation expresses five different forms of the KdV equation, each of these equations has different applications in many fields, including fluid mechanics, ocean science and optics. We utilized Painlevé property for the governing equation to prove that the equation possesses Painlevé test. Then, the symmetry method is used to study the similarity reductions for the governing equation. Subsequently, we obtained a novel type of exact solutions for family KdV fifth-order by using (G′/G)-expansion method. The obtained solutions included hyperbolic and trigonometric functions. The solutions are also presented in 3D shapes to show their properties contained kink wave, singular wave, anti-kink wave, periodic wave and solitary wave solution.

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Published

30-11-2024
CITATION

How to Cite

Gaber, A., & Mostafa, D. M. (2024). Painlevé Analysis, Lie Symmetries and Abundant Wave Solutions for Family Fifth Order Kdv Equations. Communications in Mathematics and Applications, 15(3), 1231–1240. https://doi.org/10.26713/cma.v15i3.2752

Issue

Vol. 15 No. 3 (2024)

Section

Research Article

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