Wave solitons are stable, localized wave packets that maintain their shape while traveling at constant speeds. They occur in various physical systems, such as water waves, optical fibers, and plasma. Solitons arise due to a balance between nonlinearity and dispersion, allowing them to resist the tendency to spread out over time. These unique wave phenomena were first discovered in the context of fluid dynamics by John Scott Russell in the 19th century. Solitons have important applications in fields like fiber optics, where they can enhance data transmission, and in nonlinear optics, where they help in the study of light behavior in different media.