Wave maps equation

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

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

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

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

References

  1. Tataru, Daniel (1 January 2005). "Rough solutions for the wave maps equation". American Journal of Mathematics. 127 (2): 293–377. doi:10.1353/ajm.2005.0014. S2CID 53521030.
  2. Tataru, Daniel (2004). "The wave maps equation" (PDF). Bulletin of the American Mathematical Society. New Series. 41 (2): 185–204. doi:10.1090/S0273-0979-04-01005-5. Zbl 1065.35199.
  3. Tao, Terence. "Wave Maps (preprint)" (PDF). Department of Mathematics, UCLA. Retrieved 2023-10-04.