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.
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