On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions

Atsushi Nakayashiki

Symmetry, integrability and geometry: methods and applications, Tome 15 (2019)

Résumé

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.

Détail

Keywords: hyperelliptic curve; soliton solution; KP hierarchy; Sato Grassmannian.

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