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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)

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
Full Text: DOI arXiv
[1] DOI: 10.1007/BF02725674 · doi:10.1007/BF02725674
[2] DOI: 10.1016/S0375-9601(96)00709-8 · Zbl 1037.83505 · doi:10.1016/S0375-9601(96)00709-8
[3] DOI: 10.1016/0550-3213(81)90006-7 · Zbl 1258.81046 · doi:10.1016/0550-3213(81)90006-7
[4] DOI: 10.1142/S0217751X90000647 · doi:10.1142/S0217751X90000647
[5] DOI: 10.1063/1.1703993 · Zbl 0133.34202 · doi:10.1063/1.1703993
[6] DOI: 10.1137/1029003 · Zbl 0656.34028 · doi:10.1137/1029003
[7] DOI: 10.1007/BF02507892 · doi:10.1007/BF02507892
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