Method of comparison equations and generalized Ermakov's equation
Abstract
The connection between the method of comparison equations (generalized WKB method) and the ErmakovPinney equation is established. A perturbative scheme of solution of the generalized ErmakovPinney equation is developed and is applied to the construction of perturbative series for secondorder differential equations with and without turning points.
 Publication:

Russian Physics Journal
 Pub Date:
 December 2009
 DOI:
 10.1007/s1118201093754
 arXiv:
 arXiv:mathph/0506017
 Bibcode:
 2009RuPhJ..52.1339K
 Keywords:

 Ermakov’s equation;
 semiclassical approach;
 comparison functions;
 Mathematical Physics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 The collective of the authors is enlarged and the calculations in Sec. 3 are corrected