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arXiv · 2502.19972

Hyperelliptic sigma functions and the Kadomtsev-Petviashvili equation

Takanori Ayano·Victor M. Buchstaber
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Abstract

In this paper, a theory of hyperelliptic functions based on multidimensional sigma functions is developed and explicit formulas for hyperelliptic solutions to the Kadomtsev-Petviashvili equations KP-I and KP-II are obtained. The long-standing problem of describing the dependence of these solutions on the variation of the coefficients of the defining equation of a hyperelliptic curve, which are integrals of the equations, is solved.

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BibTeXRIS

Takanori Ayano, Victor M. Buchstaber. 2025-02-27. Hyperelliptic sigma functions and the Kadomtsev-Petviashvili equation. https://doi.org/10.1016/j.physd.2025.134819

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