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Supersymmetric Quantum Mechanics and Painlevé IV Equation
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: supersymmetric quantum mechanics; Painlevé equations. 
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     author = {David Berm\'udez and David J. Fern\'andez C.},
     title = {Supersymmetric {Quantum} {Mechanics} and {Painlev\'e} {IV} {Equation}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a24/}
}
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David Bermúdez; David J. Fernández C. Supersymmetric Quantum Mechanics and Painlevé IV Equation. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a24/

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