Separation of variables in the two-dimensional wave equation with potential - Zhdanov, R.Z.; Revenko, I.V.; Fushchych, W.I. (Український математичний журнал, 1994)
The paper is devoted to solution of a problem of separation of variables in the wave equation utt−uxx+V(x)u=0. We give a complete classification of potentials V(x) for which this equation admits a nontrivial separation of variables. Furthermore, we obtain all coordinate systems that provide separability of the equation considered.