Analysis reveals differential equations for hyperelliptic functions in genus two curves, indicating connections between Jacobi type and Weierstrass functions.
We generalized the mKdV equation in order that the static equations include sn differential equation. As a result, a good correspondence was obtained between the KdV equation and the mKdV equation.For general genus two hyperelliptic curves, we obtained differential equations for Weierstrass type and Jacobi type hyperelliptic functions. Considering the special case of λ₆=0, λ₀=0, Weierstrass type and Jacobi type hyperelliptic functions are different solutions to the same hyperelliptic differential equations. Then these solutions are connected by the special Sp(4, R) Lie group transformation.
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Hayashi et al. (2025) studied this question.
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