SUSY partners of the truncated oscillator, Painlevé transcendents and Bäcklund transformations
arXiv:1603.05173 · doi:10.1088/1751-8113/49/19/195202
Abstract
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 non-linear differential equations and the Bäcklund transformations relating them.
arXiv commentThis article is a natural continuation of arXiv:1310.5628
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- Multiphoton coherent states for bilayer graphene