Solution hierarchies for the Painleve IV equation
David Bermudez, David J. Fernandez C
TL;DR
This paper develops a method to generate and classify real and complex solutions to the Painleve IV equation using supersymmetric quantum mechanics, focusing on the less-studied complex solution hierarchies.
Contribution
It introduces a novel classification of solution hierarchies for Painleve IV, expanding understanding of complex solutions through supersymmetric quantum mechanics.
Findings
Real and complex solution hierarchies constructed
New classifications of complex solutions proposed
Method demonstrates effectiveness in solution generation
Abstract
In this article we will obtain real and complex solutions to the Painleve IV equation through supersymmetric quantum mechanics. Then we will classify them into real solution hierarchies and also the complex solution hierarchies, which are hardly studied.
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