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Generalized mKdV Equation and Genus Two Jacobi Type Hyperelliptic Differential Equation

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  • Masato Hayashi
  • Kazuyasu Shigemoto
  • Takuya Tsukioka

Abstract

We generalized the mKdV equation such that the static equations included the sn differential equation. As a result, a good correspondence was obtained between the KdV and mKdV equations. For the general genus two hyperelliptic curves, we obtained differential equations for the Weierstrass-type and Jacobi-type hyperelliptic functions. Considering the special case of λ6 = 0, λ0 = 0, the Weierstrass-type and Jacobi-type hyperelliptic functions are different solutions to the same hyperelliptic differential equations. These solutions are then connected via a special Sp (4, R) Lie group transformation.

Suggested Citation

  • Masato Hayashi & Kazuyasu Shigemoto & Takuya Tsukioka, 2026. "Generalized mKdV Equation and Genus Two Jacobi Type Hyperelliptic Differential Equation," European Journal of Mathematics and Statistics, European Open Science, vol. 7(4), pages 8-14, November.
    • Handle: RePEc:epw:ejmath:v:7:y:2026:i:4:id:70828
    DOI: 10.24018/ejmath.2026.7.4.70828
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