Traveling wave solutions of nonlinear evolution equations via the F-expansion method

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Soran University, Erbil, Iraq.

2 1. Department of Mathematics, College of Science, University of Duhok, Duhok, Iraq. \\ 2.Department of Cybersecurity, College of Engineering Technology, Alnoor University, Mosul, 41012, Iraq.

3 Department of Mathematics, Faculty of Education, Soran University, Erbil, Iraq.

Abstract

In this study, we investigate the analytical solutions of three fundamental nonlinear evolution equations: the Korteweg-de Vries (KdV) equation, the modified Korteweg-de Vries (mKdV) equation, and the variant Boussinesq equations using the F-expansion method. Despite extensive research on these equations, significant gaps remain in understanding their complete solution structures and dynamic behaviors under various parametric conditions. By applying the F-expansion technique combined with traveling wave transformations, we derive multiple families of exact analytical solutions exhibiting diverse wave phenomena. The solutions are comprehensively visualized through 2D and 3D graphical representations, demonstrating rich wave dynamics and temporal evolution patterns across different parameter regimes. Additionally, we conduct detailed bifurcation analysis using phase portrait techniques and investigate chaotic behaviors through Lyapunov exponent calculations, Poincar'{e} sections, and multistability analysis, revealing complex dynamical structures including equilibrium points and chaotic attractors. The conformable derivative framework is employed to show the influence of fractional parameters on solution behavior. These models are particularly valuable for applications in nonlinear optics, where soliton solutions represent stable pulse propagation in optical fiber communications, plasma physics for ion-acoustic wave phenomena, fluid dynamics for shallow water wave modeling, and wave energy harvesting technologies. The findings contribute to advancing theoretical understanding of nonlinear wave phenomena while providing practical insights for engineering applications in modern optical communication systems and energy conversion technologies.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 07 November 2025

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History

  • Receive Date: 12 March 2025
  • Revise Date: 22 September 2025
  • Accept Date: 02 November 2025

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