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

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 $\theta$-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.

AMS-Tex, 13 pages

References in corpus (5)

• Quasi-Periodic and Periodic Solutions for Systems of Coupled Nonlinear SCHRÖdinger Equations
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