Traveling Wave Solution Method For The Generalized Kuramoto-Sivashinsky Equation

Abstract

The generalized Kuramoto-Sivashinsky (GKS) equation is an important nonlinear partial differential equation (PDE) that models various physical phenomena, including plasma instabilities, reaction-diffusion systems, and flame front propagation. This thesis explores the application of the Traveling Wave Solution Method (TWSM) to derive exact solutions for the GKS equation. By transforming the generalized Kuramoto- Sivashinsky equation into an ordinary differential equation (ODE) using a traveling wave transformation, both solitary wave and periodic solutions were obtained. The study also identifies the criteria for the existence of physical solutions and graphically illustrates the behavior of wave solutions under different conditions. The findings confirm that TWSM is an effective tool for solving nonlinear PDEs, offering new insights into the complex dynamics described by the generalized Kuramoto-Sivashinsky equation