Separation of variables in two-dimensional wave equations with potential - Fushchich, V. I.; Revenko, I. V.; Zhdanov, R. Z. (Ukrains’kyi Matematychnyi Zhurnal, 1994)
The paper is devoted to solution of a problem of separation of variables in the wave equation u_tt - u_xx + 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.