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Separation of variables in two-dimensional wave equations with potential

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In the present paper, we solve the problem of separation of variables in the wave equationu tt u xx +V(x)u=0 and give a complete classification of potentialsV(x) forwhich equations of this type admit nontrivial separation of variables. Furthermore, we construct all coordinate systems in which this separation is possible.

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Published in Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1343–1361, October, 1994.

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Zhdanov, R.Z., Revenko, I.V. & Fushchich, V.I. Separation of variables in two-dimensional wave equations with potential. Ukr Math J 46, 1480–1503 (1994). https://doi.org/10.1007/BF01066092

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  • Coordinate System
  • Wave Equation
  • Complete Classification