Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation

Details Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation

2005-06-08

arxiv.org/abs/math-ph/0506017v2

Russ.Phys.J.52:1339-1351,2009

Physics

Mathematical Physics

The collective of the authors is enlarged and the calculations in Sec. 3 are corrected

Scientific paper

10.1007/s11182-010-9375-4

The connection between the method of comparison equations (generalized WKB
method) and the Ermakov-Pinney equation is established. A perturbative scheme
of solution of the generalized Ermakov-Pinney equation is developed and is
applied to the construction of perturbative series for second-order
differential equations with and without turning points.

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