308 citations · 894 across the 32 of their papers we have counts for
34 papers
Tau Functions of (n,1) curves and Soliton Solutions on Non-Zero Constant Backgrounds
Atsushi Nakayashiki
We study the tau function of the KP-hierarchy associated with an (n,1) curve . If the corresponding tau function is 1. On the other hand if the tau functio…
One Step Degeneration of Trigonal Curves and Mixing of Solitons and Quasi-Periodic Solutions of the KP Equation
Atsushi Nakayashiki
We consider certain degenerations of trigonal curves and hyperelliptic curves, which we call one step degeneration. We compute the limits of corresponding quasi-periodic solutions…
Sato Grassmannian and Degenerate Sigma Function
Julia Bernatska, Victor Enolski, Atsushi Nakayashiki
The degeneration of the hyperelliptic sigma function is studied. We use the Sato Grassmannian for this purpose. A simple decomposition of a rational function gives a decomposition…
On Reducible Degeneration of Hyperelliptic Curves and Soliton Solutions
Atsushi Nakayashiki
In this paper we consider a reducible degeneration of a hyperelliptic curve of genus . Using the Sato Grassmannian we show that the limits of hyperelliptic solutions of the KP-h…
Degeneration of Trigonal Curves and Solutions of the KP-Hierarchy
Atsushi Nakayashiki
It is known that soliton solutions of the KP-hierarchy corresponds to singular rational curves with only ordinary double points. In this paper we study the degeneration of theta fu…
On the Expansion Coefficients of KP Tau Function
Atsushi Nakayashiki, Soichi Okada, Yoko Shigyo
We study the expansion coefficients of the tau function of the KP hierarchy. If the tau function does not vanish at the origin, it is known that the coefficients are given by Giamb…