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Hyperelliptic Solutions of Modified Korteweg-de Vries Equation of Genus g: Essentials of Miura Transformation

Shigeki Matsutani
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Abstract

Explicit hyperelliptic solutions of the modified Korteweg-de Vries equations without any ambiguous parameters were constructed in terms only of the hyperelliptic $\al$-functions over non-degenerated hyperelliptic curve $y^2 = f(x)$ of arbitrary genus $g$. In the derivation, any $θ$-functions or Baker-Akhiezer functions were not essentially used. Then the Miura transformation naturally appears as the connections between the hyperelliptic $\wp$-functions and hyperelliptic $\al$-functions.

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Shigeki Matsutani. 2002-02-25. Hyperelliptic Solutions of Modified Korteweg-de Vries Equation of Genus g: Essentials of Miura Transformation. https://doi.org/10.1088/0305-4470%2F35%2F19%2F312

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