On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions

2018/08/31 by Atsushi Nakayashiki · 1 citation
Physics and Astronomy · Mathematics · #nlin.SI #math-ph #math.AG #math.MP #math.QA #msc:37K40 #msc:37K10 #msc:14H70

paper · pdf · doi:10.3842/sigma.2019.009

published as SIGMA 15 (2019), 009, 18 pages

arxiv created 2019/02/08 · arxiv updated 2019/02/11

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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