Well title says it all pretty much. My question is if one set of boundary conditions uniquely specifies the solutions to the wave equation. My speculation comes from the fact that my book introduces electromagnetic in a bit weird way I think. It shows how Maxwells equations lead to the wave equation but it then confines it interest to just plane waves of the simplest form since they solve the wave equation. But what about other kinds of waves that solve the wave equation? Are they not interesting? I am not only talking about other kinds as in spherical waves etc. but also just of waves which dont have the boring form cos(kr - ωt) but maybe just something like cos(2kr - ωt) or whatever you can make up. Because generally as I see it you can't just absorb the 2 into k since that would ruin the nice relation between ω and k.