Examples of the time-dependent linear wave equation

I am looking for examples of the non-autonomous linear wave equation that have some relevant applications.

What articles and sources (maybe, some catalogue like Handbook of Nonlinear Partial Differential Equations) may I refer to?

• I would think that you need nonlinearity for interesting/nontrivial dynamics. – Carlo Beenakker Sep 20 '17 at 9:53
• The wave equation on any non-stationary Lorentzian spacetime (that is, $\square_g u = \frac{1}{\sqrt{|\det g|}} \partial_i g^{ij} \sqrt{|\det g|} \partial_j u = 0$ for a Lorentzian metric $g_{ij}$) is an example. You can read about the (abstract) theory of such equations, for instance, in this book. If you are looking for a list of interesting Lorentzian manifolds, you may want to take a look at this book. – Igor Khavkine Sep 20 '17 at 10:42