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
