Separation of variables in two-dimensional wave equations with potential

• Date: 1994
• Main Authors: Fushchich, V. I., Revenko, I. V., Zhdanov, R. Z., Фущич, В. І., Ребенко, І. В., Жданов, Р. З.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 1994
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5613
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 tha...