139 citations · 245 across the 9 of their papers we have counts for
9 papers
A study on the bilinear equation of the sixth Painlevé transcendents
Tatsuya Hosoi, Hidetaka Sakai
The sixth Painlevé equation is a basic equation among the non-linear differential equations with three fixed singularities, corresponding to Gauss's hypergeometric differential equ…
Discrete Hamiltonians of discrete Painlevé equations
Takafumi Mase, Akane Nakamura, Hidetaka Sakai
We express discrete Painlevé equations as discrete Hamiltonian systems. The discrete Hamiltonian systems here mean the canonical transformations defined by generating functions. Ou…
CFT approach to the -Painlevé VI equation
M. Jimbo, H. Nagoya, H. Sakai
Iorgov, Lisovyy, and Teschner established a connection between isomonodromic deformation of linear differential equations and Liouville conformal field theory at . In this pap…
Spectral types of linear -difference equations and -analog of middle convolution
Hidetaka Sakai, Masashi Yamaguchi
We give a -analog of middle convolution for linear -difference equations with rational coefficients. In the differential case, middle convolution is defined by Katz, and he e…
Discrete Schlesinger Transformations, their Hamiltonian Formulation, and Difference Painlevé Equations
Anton Dzhamay, Hidetaka Sakai, Tomoyuki Takenawa
Schlesinger transformations are algebraic transformations of a Fuchsian system that preserve its monodromy representation and act on the characteristic indices of the system by int…
Degeneration scheme of 4-dimensional Painlevé-type equations
Hiroshi Kawakami, Akane Nakamura, Hidetaka Sakai
Four 4-dimensional Painlevé-type equations are obtained by isomonodromic deformation of Fuchsian equations: they are the Garnier system in two variables, the Fuji-Suzuki system, th…
Riccati Solutions of Discrete Painlevé Equations with Weyl Group Symmetry of Type
Mikio Murata, Hidetaka Sakai, Jin Yoneda
We present a special solutions of the discrete Painlevé equations associated with , and -surface. These solutions can be expressed by solutions…
Bilinear structure and Schlesinger transforms of the -P and -P equations
M. Jimbo, H. Sakai, A. Ramani +1
We show that the recently derived (-) discrete form of the Painlevé VI equation can be related to the discrete P, in particular if one uses the full freedom in the i…
A -anaolg of the sixth Painlevé equation
Michio Jimbo, Hidetaka Sakai
A -difference analog of the sixth Painlevé equation is presented. It arises as the condition for preserving the connection matrix of linear -difference equations, in close an…