I'm reading Jackson's Electrodynamics chapter 6.2.
It is possible to reduce Maxwell's equations to
$\nabla^2 \phi + \frac{\partial}{\partial t} (\nabla \cdot A) = - \frac{\rho}{\epsilon_0}$ (6.10)
$\nabla^2 A - \frac{1}{c^2} \frac{\partial^2 A}{\partial t^2} - \nabla( \nabla \cdot A + \frac{1}{c^2} \frac{\partial \phi}{\partial t }) = - \mu_0 J$ (6.11)
By satisfying Lorenz condition
One can uncouple into
$\nabla^2 \phi - \frac{1}{c^2} \frac{\partial^2 \phi}{\partial t^2} = \frac{- \rho}{\epsilon_0}$
$\nabla^2 A - \frac{1}{c^2} \frac{\partial^2 A}{\partial t^2} = - \mu_0 J$
I have not seen this kind of thing outside of the context of electromagnetism. Is there a more general name for this kind of thing in mathematics for uncoupling pde?