Painlevé analysis, Lie symmetries and abundant wave solutions for family fifth order KdV equations

family fifth order KdV equations

Authors

  • Ahmed Gaber Partial differential equations
  • Doaa M Mostafa 2Department of Mathematics, College of Science, Qassim University, P. O. Box 6644, Buraidah 51452, Saudi Arabia

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 have different applications in many fields, including: fluid mechanics, oceans science and optics. We utilized Painlevé property for governing equation to prove that the equation possessing Painleve test. Then, 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 that contained kink wave, singular wave, anti-kink wave, periodic wave and solitary wave solution.

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Published

20-02-2025

How to Cite

Gaber, A., & M Mostafa, D. . (2025). Painlevé analysis, Lie symmetries and abundant wave solutions for family fifth order KdV equations: family fifth order KdV equations. Communications in Mathematics and Applications, 15(3). Retrieved from https://rgnpublications.com/journals/index.php/cma/article/view/2752

Issue

Vol. 15 No. 3 (2024)

Section

Research Article

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