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arXiv · 1808.06748

On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions

Atsushi Nakayashiki
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Abstract

In this paper we consider a reducible degeneration of a hyperelliptic curve of genus $g$. Using the Sato Grassmannian we show that the limits of hyperelliptic solutions of the KP-hierarchy exist and become soliton solutions of various types. We recover some results of Abenda who studied regular soliton solutions corresponding to a reducible rational curve obtained as a degeneration of a hyperelliptic curve. We study singular soliton solutions as well and clarify how the singularity structure of solutions is reflected in the matrices which determine soliton solutions.

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BibTeXRIS

Atsushi Nakayashiki. 2018-08-21. On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions. https://doi.org/10.3842/sigma.2019.009

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