2019
Том 71
№ 11

# Separation of variables in two-dimensional wave equations with potential

Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 46 (1994), no. 10, pp 1480-1503.

Citation Example: Fushchich V. I., Revenko I. V., Zhdanov R. Z. Separation of variables in two-dimensional wave equations with potential // Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1343–1361.

Full text