Integral transformation and Darboux transformation
arXiv:0911.2162 · doi:10.1063/1.3367079
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.
7 pages, based on the talk presented at International Workshop on Nonlinear and Modern Mathematical Physics, China, 19th July 2009