Bermúdez, David; C., David J. Fernández Supersymmetric quantum mechanics and Painlevé IV equation. (English) Zbl 1217.81098 SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 025, 14 p. (2011). Summary: As it has been proven, the determination of general one-dimensional Schrödinger Hamiltonians having third-order differential ladder operators requires to solve the Painlevé IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a simple technique for generating solutions of the Painlevé IV equation. Finally, we classify these solutions into three relevant hierarchies. Cited in 14 Documents MSC: 81Q60 Supersymmetry and quantum mechanics 35G20 Nonlinear higher-order PDEs 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies Keywords:supersymmetric quantum mechanics; Painlevé equations PDFBibTeX XMLCite \textit{D. Bermúdez} and \textit{D. J. F. C.}, SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 025, 14 p. (2011; Zbl 1217.81098) Full Text: DOI arXiv EuDML