Аннотация:
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.
Ключевые слова:
hyperelliptic curve; soliton solution; KP hierarchy; Sato Grassmannian.
\RBibitem{Nak19}
\by Atsushi~Nakayashiki
\paper On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions
\jour SIGMA
\yr 2019
\vol 15
\papernumber 009
\totalpages 18
\mathnet{http://mi.mathnet.ru/sigma1445}
\crossref{https://doi.org/10.3842/SIGMA.2019.009}
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Эта публикация цитируется в следующих 5 статьяx:
Takashi Ichikawa, “Periods of Tropical Curves and Associated KP Solutions”, Commun. Math. Phys., 402:2 (2023), 1707
Yuji Kodama, Yuancheng Xie, “Space Curves and Solitons of the KP Hierarchy. I. The $l$-th Generalized KdV Hierarchy”, SIGMA, 17 (2021), 024, 43 pp.
A. Nakayashiki, “Tau functions of $(n, 1)$ curves and soliton solutions on nonzero constant backgrounds”, Lett. Math. Phys., 111:3 (2021), 85
S. Abenda, “Kasteleyn theorem, geometric signatures and KP-II divisors on planar bipartite networks in the disk”, Math. Phys. Anal. Geom., 24:4 (2021), 35
Bernatska J. Enolski V. Nakayashiki A., “Sato Grassmannian and Degenerate SIGMA Function”, Commun. Math. Phys., 374:2 (2020), 627–660
Цитирование в формате AMSBIB
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