Finding solutions of some partial differential equations with the sine-gordon expansion method

This thesis consists of five main sections. In the first section, the fundamental principles of the Sine-Gordon expansion method, its theoretical framework, and application processes are comprehensively explained. The second section addresses the basic definitions and conceptual framework used in the study. The third section provides a detailed analysis of the structural properties of the Sine-Gordon expansion method. In the fourth section, the Sine-Gordon expansion method (SGEM) is applied to solve various equations, including the Camassa-Choi (CC) equation, the (2+1) dimensional Wazwaz-Kaur-Boussinesq (WKB) equation, and the thin-film ferroelectric materials (TFFEM) equation. Additionally, the semi analytical solutions obtained are visualized through three-dimensional, two-dimensional, contour, and density plots using Mathematica 12 software. Finally, the fifth and last section presents a detailed evaluation of the findings, and the overall results are discussed in light of these findings.