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arXiv · 1006.5185

Mathieu equation and Elliptic curve

Wei He·Yan-Gang Miao
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Abstract

We present a relation between the Mathieu equation and a particular elliptic curve. We find that the Floquet exponent of the Mathieu equation, for both $q<<1$ and $q>>1$, can be obtained from the integral of a differential one form along the two homology cycles of the elliptic curve. Certain higher order differential operators are needed to generate the WKB expansion. We provide a fifth order proof.

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Wei He, Yan-Gang Miao. 2011-03-20. Mathieu equation and Elliptic curve. https://doi.org/10.1088/0253-6102%2F58%2F6%2F08

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