SUSY partners of the truncated oscillator, Painlevé transcendents and Bäcklund transformations

In this work the supersymmetric technique is applied to the truncated oscillator to generate Hamiltonians ruled by second and third-order polynomial Heisenberg algebras, which are connected to the Painlevé IV and Painlevé V equations respectively. The aforementioned connection is exploited to produce particular solutions to both nonlinear differential equations and the Bäcklund transformations relating them. (paper)