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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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4 Aug 2001 | | Subject: | Exactly Solvable and Integrable Systems; Mathematical Physics; Algebraic Geometry | nlin.SI math-ph math.AG math.MP | | 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 $ heta$-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. | | Source: | arXiv, nlin.SI/0108002 | | Services: | Forum | Review | PDF | Favorites | |
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