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.