Heun Equation and Painlevé Equation
نویسنده
چکیده
We relate two parameter solutions of the sixth Painlevé equation and finite-gap solutions of the Heun equation by considering monodromy on a certain class of Fuchsian differential equations. In the appendix, we present formulae on differentials of elliptic modular functions, and obtain the ellitic form of the sixth Painlevé equation directly.
منابع مشابه
Elliptic Integrable Systems Heun Equation and Painlevé Equation
We relate two parameter solutions of the sixth Painlevé equation and finitegap solutions of the Heun equation by considering monodromy on a certain class of Fuchsian differential equations. In the appendix, we present formulae on differentials of elliptic modular functions, and obtain the ellitic form of the sixth Painlevé equation directly.
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