Ultrahyperbolic equation

In the mathematical field of partial differential equations, the ultrahyperbolic equation is a partial differential equation for an unknown scalar function u of 2n variables x₁, ..., x_n, y₁, ..., y_n of the form

More generally, if a is any quadratic form in 2n variables with signature (n,n), then any PDE whose principal part is is said to be ultrahyperbolic. Any such equation can be put in the form 1. above by means of a change of variables.