467 citations · 2k across the 86 of their papers we have counts for
86 papers
Direct linearization, Cauchy matrix and Sato Grassmannian
Kanehisa Takasaki
Fu and Nijhoff's direct linearization scheme for the KP hierarchy and its reductions employs a system of evolution equations of an infinite matrix with quadratic nonlinearity.…
Generalized ILW hierarchy: Solutions and limit to extended lattice GD hierarchy
Kanehisa Takasaki
The intermediate long wave (ILW) hierarchy and its generalization, labelled by a positive integer , can be formulated as reductions of the lattice KP hierarchy. The integrabilit…
Extended lattice Gelfand-Dickey hierarchy
Kanehisa Takasaki
The lattice Gelfand-Dickey hierarchy is a lattice version of the Gelfand-Dickey hierarchy. A special case is the lattice KdV hierarchy. Inspired by recent work of Buryak and Rossi,…
Dressing operators in equivariant Gromov-Witten theory of
Kanehisa Takasaki
Okounkov and Pandharipande proved that the equivariant Toda hierarchy governs the equivariant Gromov-Witten theory of . A technical clue of their method is a pair of…
Integrable structures of specialized hypergeometric tau functions
Kanehisa Takasaki
Okounkov's generating function of the double Hurwitz numbers of the Riemann sphere is a hypergeometric tau function of the 2D Toda hierarchy in the sense of Orlov and Scherbin. Thi…
Cubic Hodge integrals and integrable hierarchies of Volterra type
Kanehisa Takasaki
A tau function of the 2D Toda hierarchy can be obtained from a generating function of the two-partition cubic Hodge integrals. The associated Lax operators turn out to satisfy an a…