Soliton Solutions of Kortweg-de Vries Equations and Hyperelliptic Sigma Functions

Abstract

Soliton Solutions of Korteweg-de Vries (KdV) were constructed for given degenerate curves $y^2=(x-c)P(x{)}^2$ in terms of hyperelliptic sigma functions and explicit Abelian integrals. Connection between sigma functions and tau function were also presented.

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