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The nonlinear superposition principle and the Wei-Norman method. (English) Zbl 0928.34025
Authors’ abstract: “Group theoretical methods are used to study some properties of the Riccati equation, which is the only differential equation admitting a nonlinear superposition principle. The Wei-Norman method is applied to obtain the associated differential equation in the group $$SL(2,\mathbb{R})$$. The superposition principle for first-order differential equation systems and the Lie-Scheffers theorem are analyzed from this group theoretical perspective. Finally, the theory is applied in the solution of second-order differential equations like time-independent Schrödinger equation”.
Reviewer: S.Mazanik (Minsk)

##### MSC:
 34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 34A34 Nonlinear ordinary differential equations and systems, general theory
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##### References:
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