Abstract
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.
Mathematics Subject Classification (2010). Primary 34M55; Secondary 81Q60.
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© 2016 Springer International Publishing Switzerland
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Fernández C., D.J. (2016). Painlevé Equations and Supersymmetric Quantum mechanics. In: Kielanowski, P., Ali, S., Bieliavsky, P., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-31756-4_18
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DOI: https://doi.org/10.1007/978-3-319-31756-4_18
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-31755-7
Online ISBN: 978-3-319-31756-4
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