Shigeki Matsutani 2001 J. Phys. A: Math. Gen. 34 4721 doi:10.1088/0305-4470/34/22/312
Hyperelliptic solutions of KdV and KP equations: re-evaluation of Baker's study on hyperelliptic sigma functions
Shigeki Matsutani
Show affiliations Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV) and Kadomtsev-Petviashvili (KP) equations are constructed for a given curve y2 = f(x) whose genus is three. This paper is based upon the fact that 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 differential operator D, identities of Pfaffians, symmetric functions, the hyperelliptic σ-function and 
-functions; µν = -∂µ∂νlog σ = -(DµDνσσ)/2σ2. The connection between his theory and the modern soliton theory is also discussed.
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Issue 22 (8 June 2001)
Received 30 August 2000, in final form 28 February 2001
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Hyperelliptic solutions of KdV and KP equations: re-evaluation of Baker's study on hyperelliptic sigma functions
Shigeki Matsutani 2001 J. Phys. A: Math. Gen. 34 4721
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