Soliton Solutions of Kortweg-de Vries Equations and Hyperelliptic Sigma Functions
classification
🧮 math-ph
math.AGmath.APmath.MPnlin.SI
keywords
functionssigmahyperellipticsolitonsolutionsvrieswereabelian
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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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