Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker’s Study on Hyperelliptic Sigma Functions
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چکیده
Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV) and Kadomtsev-Petviashvili (KP) equations were constructed for a given curve y = 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∂ν log σ = −(DμDνσσ)/2σ. The connection between his theory and the modern soliton theory was also discussed.
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تاریخ انتشار 2008