  In order to find higher dimensional integrable models, we study differential
equations of hyperelliptic $\wp$ functions up to genus four. For genus two,
differential equations of hyperelliptic $\wp$ functions can be written in the
Hirota form. If the genus is more than one, we have KdV equation. If the genus
is more than two, we have KdV and another KdV equations. If the genus becomes
more than three, there appear differential equations which cannot be written in
the Hirota form, which means that the Hirota form is not enough to characterize
the integrable differential equations. We have shown that some differential
equations are satisfied for general genus. We can obtain differential equations
for general genus step by step.
