Periodic travelling wave

In mathematics, a periodic travelling wave (or wavetrain) is a <a href="/facts/Periodic_function/Sm8lJQsF">periodic function</a> of one-<a href="/facts/Dimension/0ktmUyac">dimensional</a> <a href="/facts/Euclidean_space/R2UbzmzM">space</a> that moves with constant speed. Consequently, it is a special type of spatiotemporal <a href="/facts/Oscillation/6vSrm84a">oscillation</a> that is a periodic function of both space and time.
Periodic travelling waves play a fundamental role in many mathematical equations, including <a href="/facts/Oscillation_theory/xSxr5zC4">self-oscillatory systems</a>, 
<a href="/facts/Excitable_medium/LSjRJ6I5">excitable systems</a> and
<a href="/facts/Convection%25E2%2580%2593diffusion_equation/jHoHG5Xj">reaction–diffusion–advection systems</a>. 
Equations of these types are widely used as <a href="/facts/Mathematical_model/CGhyuxgz">mathematical models</a> of biology, chemistry and physics, and many examples in phenomena resembling periodic travelling waves have been found <a href="/facts/Empirical_evidence/JUaYSGJc">empirically</a>.
The mathematical theory of periodic travelling waves is most fully developed for <a href="/facts/Partial_differential_equation/DyPsBlv7">partial differential equations</a>, but these solutions also occur in a number of other types of mathematical system, including integrodifferential equations, 
integrodifference equations,
coupled map lattices
and <a href="/facts/Cellular_automaton/6gfkjKAW">cellular automata</a>.
As well as being important in their own right, periodic travelling waves are significant as the one-dimensional equivalent of <a href="/facts/Spiral_wave/m57q5c9J">spiral waves</a> and target patterns in two-dimensional space, and of scroll waves in three-dimensional space.

Periodic travelling wave open-in-new

Periodic travelling wave