I was interrested in the general solutions to the wave equation depending on only one spatial coordinate. For one linear coordinate, the general solution is: a f(x-ct) + b g(x+ct) For one radial spherical coordinate, the general solution is: a f(r-ct)/r + b g(r+ct)/r I thought that for a radial cylindrical coordinate, the solution would be: a f(r-ct)*Log(r) + b g(r+ct)*Log(r) Yet I found this is not a solution since I got this residual for the wave equation: D²(f(r-ct)/r) = a (2+Log(r))*f'(r-ct)/r + b (2+Log(r))*g'(r+ct)/r This would indicate that the cylindrical solution applies only to the static case. Any comment on this surprise? Did I do a mistake in the calculations, of does that instead mean something? Thanks.