×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.