Investigation of New Solitary Wave Solutions of the Gilson-Pickering Equation Using Advanced Computational Techniques

Abstract

This study focuses on employing recent and accurate computational techniques, specifically the Sardar-sub equation [Formula: see text] method, to explore novel solitary wave solutions of the Gilson–Pickering [Formula: see text] equation. The GP equation is a mathematical model with implications in fluid dynamics and wave phenomena. It describes the behavior of solitary waves, which are localized disturbances propagating through a medium without changing shape. The physical significance of the [Formula: see text] equation lies in its ability to capture the dynamics of solitary waves in various systems, including water waves, optical fibers, and nonlinear acoustic waves. The study’s findings contribute to the advancement of mathematical modeling approaches and offer valuable insights into solitary wave phenomena. The stability of the constructed solutions is investigated using the properties of the Hamiltonian system. The accuracy of the computational solutions is demonstrated by comparing them with approximate solutions obtained through He’s variational iteration [Formula: see text] method. Furthermore, the effectiveness of the employed computational techniques is validated through comparisons with other existing methods.