Orthogonal and non-orthogonal separation of variables in the wave equation utt-uxx+V(x)u=0utt-uxx+V(x)u=0
- 7 November 1993
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 26 (21) , 5959-5972
- https://doi.org/10.1088/0305-4470/26/21/033
Abstract
We develop a direct approach to the separation of variables in partial differential equations. Within the framework of this approach, the problem of the separation of variables in the wave equation with time-independent potential reduces to solving an over-determined system of nonlinear differential equations. We have succeeded in constructing its general solution and, as a result, all potentials V(x) permitting variable separation have been found. For each of them we have constructed all inequivalent coordinate systems providing separability of the equation under study. It should be noted that the above approach yields both orthogonal and non-orthogonal systems of coordinates.Keywords
This publication has 8 references indexed in Scilit:
- On the reduction of the nonlinear multi-dimensional wave equations and compatibility of the d'Alembert-Hamilton systemJournal of Mathematical Analysis and Applications, 1991
- The rotational distribution of OCS+(Ã 2ΠΩ: 00) arising from the thermal energy charge transfer reaction of N2+ with OCSChemical Physics Letters, 1987
- The symmetry and some exact solutions of the nonlinear many-dimensional Liouville, d'Alembert and eikonal equationsJournal of Physics A: General Physics, 1983
- A precise definition of separation of variablesPublished by Springer Nature ,1980
- On the separability of the sine-Gordon equation and similar quasilinear partial differential equationsJournal of Mathematical Physics, 1978
- Lie theory and separation of variables. 11. The EPD equationJournal of Mathematical Physics, 1976
- Lie theory and separation of variables. 3. The equation ftt−fss =γ2fJournal of Mathematical Physics, 1974
- Separable Systems of StackelAnnals of Mathematics, 1934