Analytical and numerical investigation of soliton wave solutions in the fifth-order KdV equation within the KdV-KP framework

Abstract

This study investigates the fifth-order Korteweg–de Vries (fKdV) equation, which is a generalized form of the classical KdV equation governing weakly nonlinear waves in dispersive media. By employing analytical and numerical techniques, the Khater II and variational iteration methods are utilized to obtain accurate soliton wave solutions. The combination of these approaches ensures the reliability and precision of the analytical outcomes. Graphical representations, including two-dimensional, three-dimensional, and contour plots, visually illustrate the results. Additionally, the stability of the constructed solutions is assessed through the characterization of the Hamiltonian system, providing valuable insights into the soliton wave solutions’ stability properties. This research integrates analytical and numerical methods to explore the fKdV equation within the KdV-KP framework, offering novel soliton wave solutions and enhancing their interpretation through graphical representations while assessing their stability using the Hamiltonian system’s characterization.