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

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

2001-08-04

arxiv.org/abs/nlin/0108002v6

Nonlinear Sciences

Exactly Solvable and Integrable Systems

AMS-Tex, 13 pages

Scientific paper

10.1088/0305-4470/35/19/312

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 $\theta$-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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