Painlevé Equations and Supersymmetric Quantum mechanics

  • David J. Fernández C.
Conference paper
Part of the Trends in Mathematics book series (TM)


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.


Painlevé equations supersymmetric quantum mechanics polynomial Heisenberg algebras 


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Physics Department, CinvestavMéxico D.F.Mexico

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