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High Quality Content by WIKIPEDIA articles! In the mathematical field of partial differential equations, the ultrahyperbolic wave equation is a partial differential equation. The ultrahyperbolic wave equation has been studied from a number of viewpoints. On the one hand, it resembles the classical wave equation. This has led to a number of developments concerning its characteristics, one of which is due to Fritz John: the John equation. The equation has also been studied from the point of view of symmetric spaces, and elliptic differential operators. In particular, the ultrahyperbolic wave equation satisfies an analog of the mean value theorem for harmonic functions.