  Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV)
and \break Kadomtsev-Petviashvili (KP) equations were constructed for a given
curve $y^2 = f(x)$ whose genus is three. This study was based upon the fact
that about one hundred years ago (Acta Math. (1903) {\bf{27}}, 135-156), H. F.
Baker essentially derived KdV hierarchy and KP equation by using bilinear
differential operator ${\bold{D}}$, identities of Pfaffians, symmetric
functions, hyperelliptic $\sigma$-function and $\wp$-functions; $\wp_{\mu \nu}
= -\partial_\mu \partial_\nu \log \sigma$ $= - ({\bold{D}}_\mu {\bold{D}}_\nu
\sigma \sigma)/2\sigma^2$. The connection between his theory and the modern
soliton theory was also discussed.
