This article is cited in 15 papers

Complex SUSY transformations and the Painlevé IV equation

David Bermúdez

Departamento de Física, Cinvestav, AP 14-740, 07000 México DF, Mexico

Abstract: In this paper we will explicitly work out the complex first-order SUSY transformation for the harmonic oscillator in order to obtain both real and complex new exactly-solvable potentials. Furthermore, we will show that this systems lead us to exact complex solutions of the Painlevé IV equation with complex parameters. We present some concrete examples of such solutions.

Keywords: supersymmetric quantum mechanics; Painlevé equations; differential equations; quantum harmonic oscillator; polynomial Heisenberg algebras.

MSC: 81Q60; 35G20; 34M55

Received: July 29, 2012; in final form September 28, 2012; Published online October 11, 2012

Language: English

DOI: 10.3842/SIGMA.2012.069

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ArXiv: 1208.1782