Том 71
№ 9

All Issues

Revenko I. V.

Articles: 1
Article (English)

Separation of variables in two-dimensional wave equations with potential

Fushchich V. I., Revenko I. V., Zhdanov R. Z.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 10. - pp. 1343–1361

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.