I have been looking into the Cauchy-Kovalevskaya Theorem where one can "establish the local existence of analytic solutions to a system of PDEs".
I wanted to see an application (for example, see here) of this theorem (before going through the abstract version and getting 'lost') for higher order PDEs.
Are there any readily available worked out examples? Or perhaps, if someone could explain how the theorem can be applied to some Cauchy problem of, say, $u_{xx}-u_{yy}=0$ (or any other PDE).
Thanks, Jay.