XXXVII Workshop on Geometric Methods in Physics 1-7.07.2018
VII School on Geometry and Physics 25-29.06.2018

David Fernandez

A simple generation of Painlevé V transcendents

An algorithm for generating solutions to the Painlevé V equation, the so-called Painlevé V transcendents, is presented. One arrives to such a recipe as follows: first one looks for the general one-dimensional Schrödinger Hamiltonians ruled by third degree polynomial Heisenberg algebras (PHA), which have fourth order differential ladder operators; then one realizes that there is a key function that must satisfy the Painlevé V equation. Conversely, by identifying a system ruled by such a PHA, in particular its four extremal states, one can build this key function in a simple way. The simplest Painlevé V transcendents will be as well generated through such an algorithm.

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