Abstract
The main result of this article is that we show that from supersymmetry we can generate new superintegrable Hamiltonians. We consider a particular case with a third order integral and apply Mielnik’s construction in supersymmetric quantum mechanics. We obtain a new superintegrable potential separable in Cartesian coordinates with a quadratic and quintic integrals and also one with a quadratic integral and an integral of order of 7. We also construct a superintegrable system written in terms of the fourth Painlevé transcendent with a quadratic integral and an integral of order of 7.
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