# Wave maps equation

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In mathematical physics, the wave maps equation is a geometric wave equation that solves

The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in classical physics—such as mechanical waves or light waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics.

${\displaystyle D^{\alpha }\partial _{\alpha }u=0}$

where ${\displaystyle D}$ is a connection. [1] [2]

It can be considered a natural extension of the wave equation for Riemannian manifolds. [3]

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## References

1. Tataru, Daniel (1 January 2005). "Rough solutions for the wave maps equation". American Journal of Mathematics. 127 (2): 293–377. CiteSeerX  . doi:10.1353/ajm.2005.0014.
2. Tataru, Daniel (2004). "The wave maps equation" (PDF). Bulletin of the American Mathematical Society (N.S.) . 41 (2): 185–204. doi:10.1090/S0273-0979-04-01005-5. Zbl   1065.35199.