4 citations · 9 across the 4 of their papers we have counts for
6 papers
Tyurin parameters of commuting pairs and infinite dimensional Grassmann manifold
Kanehisa Takasaki
Commuting pairs of ordinary differential operators are classified by a set of algebro-geometric data called ``algebraic spectral data''. These data consist of an algebraic curve (`…
Elliptic spectral parameter and infinite dimensional Grassmann variety
Kanehisa Takasaki
Recent results on the Grassmannian perspective of soliton equations with an elliptic spectral parameter are presented along with a detailed review of the classical case with a rati…
Tyurin parameters and elliptic analogue of nonlinear Schrödinger hierarchy
Kanehisa Takasaki
Two "elliptic analogues'' of the nonlinear Schrödinger hiererchy are constructed, and their status in the Grassmannian perspective of soliton equations is elucidated. In addition t…
Integrable systems whose spectral curve is the graph of a function
Kanehisa Takasaki
For some integrable systems, such as the open Toda molecule, the spectral curve of the Lax representation becomes the graph of a function . Thos…
Toroidal Lie algebras and Bogoyavlensky's 2+1-dimensional equation
T. Ikeda, K. Takasaki
We introduce an extension of the \ell-reduced KP hierarchy, which we call the \ell-Bogoyavlensky hierarchy. Bogoyavlensky's 2+1-dimensional extension of the KdV equation is the low…
Gaudin Model, KZ Equation, and Isomonodromic Problem on Torus
Kanehisa Takasaki
This paper presents a construction of isospectral problems on the torus. The construction starts from an SU(n) version of the XYZ Gaudin model recently studied by Kuroki and Takebe…