Separation of variables in two-dimensional wave equations with potential

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

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.
Published
25.10.1994
How to Cite
FushchichV. I., RevenkoI. V., and ZhdanovR. Z. “Separation of Variables in Two-Dimensional Wave Equations With Potential”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 46, no. 10, Oct. 1994, pp. 1343–1361, https://umj.imath.kiev.ua/index.php/umj/article/view/5613.
Section
Research articles