A wave is an oscillation of a physical quantity around a rest value over a region of space and over time. The wave may move across space like a radio wave, in which case it is known as a traveling wave, or oscillate in place like a guitar string, in which case it is known as a standing wave. The most common kinds of waves are mechanical waves, deformations of a medium by repeated compression and decompression like sound or water waves, and electromagnetic waves, coupled oscillating electric and magnetic fields like light or radio waves.
The behavior of a wave can be modeled mathematically by numerous equations. The most important among them is the aptly-called wave equation, which has historically laid the foundation of the study of waves, starting from linear, nondispersive ones. Other equations have been developed to study more complicated processes, like dispersion and nonlinearity, either by extending the original wave equation or by starting from a completely different origin and ending up with something that resembles the wave equations (such as the Schrödinger equation).