R Z Zhdanov et al 1993 J. Phys. A: Math. Gen. 26 5959 doi:10.1088/0305-4470/26/21/033
R Z Zhdanov, I V Revenko and W I Fushchych
Show affiliationsWe 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.
02.30.Jr Partial differential equations
02.30.Hq Ordinary differential equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
35J05 Laplace equation, reduced wave equation (Helmholtz), Poisson equation (See also 31Axx, 31Bxx)
35J70 Elliptic partial differential equations of degenerate type
Issue 21 (7 November 1993)
R Z Zhdanov et al 1993 J. Phys. A: Math. Gen. 26 5959
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