Integral transformation and Darboux transformation
Kouichi Takemura
TL;DR
This paper explores the relationship between integral transformations and Darboux-Crum transformations of Heun's differential equation, highlighting their connection through elliptic functions and discussing monodromy conservation.
Contribution
It demonstrates that an integral transformation of Heun's equation generalizes the Darboux-Crum transformation using elliptic functions and analyzes monodromy preservation.
Findings
Integral transformation generalizes Darboux-Crum transformation.
Rewriting integral transformation in elliptic functions clarifies their relationship.
Monodromy is conserved under these transformations.
Abstract
We review Darboux-Crum transformation of Heun's differential equation. By rewriting an integral transformation of Heun's differential equation into a form of elliptic functions, we see that the integral representation is a generalization of Darboux-Crum transformation. We also consider conservation of monodromy with respect to the transformations.
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