Hyperelliptic solutions of KdV and KP equations: re-evaluation of Baker's study on hyperelliptic sigma functions
Journal of Physics A: Mathematical and General
Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV) and 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) 27, 135-156), H. F. Baker essentially derived KdV hierarchy and KP equation by using bilinear differential operator D, identities of Pfaffians, symmetric functions, hyperelliptic σ-function and -functions; _μν = -∂_μ∂_νσ = -
... (D_μD_νσσ)/2σ^2. The connection between his theory and the modern soliton theory was also discussed.