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(\nabla\times E(t)) &= -\mu_0\frac{\partial}{\partial t}\left(\nabla \times H\right)\\ \nabla^2 E &= \mu_0 \frac{\partial^2\varepsilon E}{\partial t^2}\\ &= \frac{\partial^2}{\partial t^2}\left(v_{ph}^2E\right) \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.