Electromagnetic wave equation with time varying phase velocity

I am attempting to solve Maxwell’s equations for the electric field of an electromagnetic wave, with time varying phase velocity, propagating within a medium within unity permeability but time varying permittivity. So far I have come up with the following derivations
begin{align}
nabla times(nablatimes E(t)) &= -mu_0frac{partial}{partial t}left(nabla times Hright)
nabla^2 E &= mu_0 frac{partial^2varepsilon E}{partial t^2}
&= frac{partial^2}{partial t^2}left(v_{ph}^2Eright)
end{align}

Are there any well-known solutions to this form of the electromagnetic wave equation? Also if there are any texts that review this form of the electromagnetic wave equation I would be ever so thankful if someone could list them.