Gaseous diffusion (GD) has been used in various fields, including electromagnetic wave fields, high-energy physics, fluid dynamics, coastal engineering, ion-acoustic waves in plasma physics, and optical fibers. GD involves random molecular movement from areas of high partial pressure to areas of low partial pressure. Researchers have developed models to describe this phenomenon, among these models is the (2 + 1)-dimensional Chaffee–Infante (CI)- equation. This research explores analytical soliton and wave solutions of Gaseous diffusion through a homogeneous medium considering two analytical methods, the Riccati equation and F-expansion methods. Thirty-seven different solutions have been identified and some of these solutions have been illustrated graphically. The figures show a range of bright, dark, singular, singular-periodic, and kink-type soliton wave solutions