Painlevé Equations and Supersymmetric Quantum mechanics
An algorithm to generate solutions to the Painlevé IV and V equations is presented, based on supersymmetric quantum mechanics applied to the harmonic and radial oscillators, respectively. These solutions are expressed in terms of confluent hypergeometric functions, leading to a classification in solution hierarchies, according to the specific special functions they involve.
KeywordsPainlevé equations supersymmetric quantum mechanics polynomial Heisenberg algebras
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