S. Matsutani, Hyperelliptic solutions of KdV and KP equations: re-evaluation of Baker's study on hyperelliptic sigma functions, J PHYS A, 34(22), 2001, pp. 4721-4732
Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (Kd
V) and Kadomtsev-Petviashvili (KP) equations are constructed for a given cu
rve y(2) = f(x) whose genus is three. This paper is based upon the fact tha
t about one hundred years ago (Baker H F 1903 Acta Math. 27 135-56;), Baker
essentially derived KdV hierarchy and KP equations by using a bilinear dif
ferential operator D, identities of Pfaffians,symmetric functions, the hype
relliptic a-function and p-functions; p(uv) = -partial derivative (mu)parti
al derivative (nu) log sigma = -(D(mu)D(nu)sigma sigma)/2 sigma (2). The co
nnection between his theory and the modern soliton theory is also discussed
.