For a burst of waves seen in quantum mechanics, see Wave packet.
In mathematics, a periodic travelling wave (or wavetrain) is a periodic function of one-dimensionalspace that moves with constant speed. Consequently, it is a special type of spatiotemporal oscillation that is a periodic function of both space and time.
The mathematical theory of periodic travelling waves is most fully developed for partial differential equations, but these solutions also occur in a number of other types of mathematical system, including integrodifferential equations,[5][6]
integrodifference equations,[7]
coupled map lattices[8]
and cellular automata[9][10]
As well as being important in their own right, periodic travelling waves are significant as the one-dimensional equivalent of spiral waves and target patterns in two-dimensional space, and of scroll waves in three-dimensional space.
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