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Complex SUSY transformations and the Painlevé IV equation
Symmetry, integrability and geometry: methods and applications, Tome 8 (2012) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {David Berm\'udez},
     title = {Complex {SUSY} transformations and the {Painlev\'e} {IV} equation},
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}
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David Bermúdez. Complex SUSY transformations and the Painlevé IV equation. Symmetry, integrability and geometry: methods and applications, Tome 8 (2012). http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a68/

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