Fuchsian equation, Hermite-Krichever Ansatz and Painlev\'e equation
Classical Analysis and ODEs
2007-05-23 v1 Mathematical Physics
math.MP
Quantum Algebra
Exactly Solvable and Integrable Systems
Abstract
Several results on Heun's equation are generalized to a certain class of Fuchsian differential equations. Namely, we obtain integral representations of solutions and develop Hermite-Krichever Ansatz on them. In particular, we investigate linear differential equations that produce Painlev\'e equation by monodromy preserving deformation and obtain solutions of the sixth Painlev\'e equation which include Hitchin's solution. The relationship with finite-gap potential is also discussed.
Cite
@article{arxiv.math/0501428,
title = {Fuchsian equation, Hermite-Krichever Ansatz and Painlev\'e equation},
author = {Kouichi Takemura},
journal= {arXiv preprint arXiv:math/0501428},
year = {2007}
}
Comments
28 pages