N. Nakazono

activity

20092026

most citedProjective reduction of the discrete Painlevé system of type

(A_{2} + A_{1})^{(1)}

18 citations · 88 across the 23 of their papers we have counts for

collaborators

24 papers

nlin.SI2026

Special solutions to five autonomous integrable partial difference equations via the third and sixth Painlevé equations and the Garnier system in two variables

Nobutaka Nakazono

In this paper, we study special solutions of five autonomous integrable partial difference equations (P $Δ$ Es). More precisely, we show that these P $Δ$ Es admit special solutions tha…

nlin.SI2025

Solutions to an autonomous discrete KdV equation via Painlevé-type ordinary difference equations

Nobutaka Nakazono

Hirota's discrete KdV equation is a well-known integrable two-dimensional partial difference equation regarded as a discrete analogue of the KdV equation. In this paper, we show th…

nlin.SI2023

A higher-order generalization of an $A_{4}^{(1)}$ -surface type $q$ -Painlevé equation with $W ((A_{2 N} ⋊ A_{1})^{(1)} \times A_{1}^{(1)})$ symmetry

Nobutaka Nakazono

Recently, a birational representation of an extended affine Weyl group of $(A_{2 N} ⋊ A_{1})^{(1)}$ -type, which gives a higher-order generalization of an $A_{4}^{(1)}$ -surface type…

nlin.SI2023

Higher-order generalizations of the $A_{6}^{(1)}$ - and $A_{4}^{(1)}$ -surface type $q$ -Painlevé equations

Nobutaka Nakazono

In this paper, we construct higher-order generalizations of the $A_{6}^{(1)}$ - and $A_{4}^{(1)}$ -surface type $q$ -Painlevé equations from the system of partial difference equations wit…

nlin.SI2022

Consistency around a cube property of Hirota's discrete KdV equation and the lattice sine-Gordon equation

Nobutaka Nakazono

It has been unknown whether Hirota's discrete Korteweg-de Vries equation and the lattice sine-Gordon equation have the consistency around a cube (CAC) property. In this paper, we s…

nlin.SI2022

Properties of the Non-Autonomous Lattice Sine-Gordon Equation: Consistency around a Broken Cube Property

Nobutaka Nakazono

The lattice sine-Gordon equation is an integrable partial difference equation on $Z^{2}$ , which approaches the sine-Gordon equation in a continuum limit. In this paper, we…

nlin.SI2021★ 2 cited

Discrete Painlevé transcendent solutions to the multiplicative type discrete KdV equations

Nobutaka Nakazono

Hirota's discrete KdV equation is an integrable partial difference equation on $Z^{2}$ , which approaches the Korteweg-de Vries (KdV) equation in a continuum limit. In this p…

nlin.SI2021★ 1 cited

On the three-dimensional consistency of Hirota's discrete Korteweg-de Vries Equation

Nalini Joshi, Nobutaka Nakazono

Hirota's discrete Korteweg-de Vries equation (dKdV) is an integrable partial difference equation on 2-dimensional integer lattice, which approaches the Korteweg-de Vries equation i…

nlin.SI2020

Reduction of quad-equations consistent around a cuboctahedron I: additive case

Nalini Joshi, Nobutaka Nakazono

In this paper, we consider a reduction of a new system of partial difference equations, which was obtained in our previous paper (Joshi and Nakazono, arXiv:1906.06650) and shown to…

nlin.SI2019

Discrete Power Functions on a Hexagonal Lattice I: Derivation of defining equations from the symmetry of the Garnier System in two variables

Nalini Joshi, Kenji Kajiwara, Tetsu Masuda +1

The discrete power function on the hexagonal lattice proposed by Bobenko et al is considered, whose defining equations consist of three cross-ratio equations and a similarity const…

nlin.SI2019★ 5 cited

Classification of quad-equations on a cuboctahedron

Nalini Joshi, Nobutaka Nakazono

In this paper, we consider polynomials associated with faces and internal quadrilaterals of a cuboctahedron and classify them under the requirement that they are consistent. These…

nlin.SI2019

A review of elliptic difference Painlevé equations

Nalini Joshi, Nobutaka Nakazono

Discrete Painlevé equations are nonlinear, nonautonomous difference equations of second-order. They have coefficients that are explicit functions of the independent variable $n$ an…

math-ph2017★ 3 cited

Geometric description of discrete power function associated with the sixth Painlevé equation

Nalini Joshi, Kenji Kajiwara, Tetsu Masuda +2

In this paper, we consider the discrete power function associated with the sixth Painlevé equation. This function is a special solution of the so-called cross-ratio equation with a…

nlin.SI2017★ 2 cited

Reduction of lattice equations to the Painlevé equations: P $_{IV}$ and P $_{V}$

Nobutaka Nakazono

In this paper, we construct a new relation between ABS equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representation…

math-ph2017★ 3 cited

Elliptic Painlevé equations from next-nearest-neighbor translations on the $E_{8}^{(1)}$ lattice

Nalini Joshi, Nobutaka Nakazono

The well known elliptic discrete Painlevé equation of Sakai is constructed by a standard translation on the $E_{8}^{(1)}$ lattice, given by nearest neighbor vectors. In this paper, w…

nlin.SI2016★ 2 cited

Reflection groups and discrete integrable systems

Nalini Joshi, Nobutaka Nakazono, Yang Shi

We present a method of constructing discrete integrable systems with crystallographic reflection group (Weyl) symmetries, thus clarifying the relationship between different discret…

math-ph2016★ 6 cited

Lattice equations arising from discrete Painlevé systems. II. $A_{4}^{(1)}$ case

Nalini Joshi, Nobutaka Nakazono, Yang Shi

In this paper, we construct two lattices from the $τ$ functions of $A_{4}^{(1)}$ -surface $q$ -Painlevé equations, on which quad-equations of ABS type appear. Moreover, using the reduc…

nlin.SI2015★ 14 cited

Geometry of an elliptic-difference equation related to Q4

James Atkinson, Phil Howes, Nalini Joshi +1

In this paper, we investigate a nonlinear non-autonomous elliptic difference equation, which was constructed by Ramani, Carstea and Grammaticos by integrable deautonomization of a…

math-ph2015★ 12 cited

Lax pairs of discrete Painlevé equations: $(A_{2} + A_{1})^{(1)}$ case

Nalini Joshi, Nobutaka Nakazono

In this paper, we provide a comprehensive method for constructing Lax pairs of discrete Painlevé equations by using a reduced hypercube structure. In particular, we consider the $A…

nlin.SI2014★ 13 cited

Lattice equations arising from discrete Painlevé systems (I): $(A_{2} + A_{1})^{(1)}$ and $(A_{1} + A_{1}^{'})^{(1)}$ cases

Nalini Joshi, Nobutaka Nakazono, Yang Shi

We introduce the concept of $ω$ -lattice, constructed from $τ$ functions of Painlevé systems, on which quad-equations of ABS type appear. In particular, we consider the $A_{5}^{(1)}$ -…

nlin.SI2013★ 4 cited

A systematic approach to reductions of type-Q ABS equations

Mike Hay, Phil Howes, Nobutaka Nakazono +1

We present a class of reductions of Möbius type for the lattice equations known as Q1, Q2, and Q3 from the ABS list. The deautonomised form of one particular reduction of Q3 is sho…

nlin.SI2013★ 2 cited

Hypergeometric solutions to the symmetric q-Painlevé equations

Kenji Kajiwara, Nobutaka Nakazono

We consider the symmetric q-Painlevé equations derived from the birational representation of affine Weyl groups by applying the projective reduction and construct the hypergeometri…

nlin.SI2013★ 1 cited

Hypergeometric Solutions of the $A_{4}^{(1)}$ -Surface $q$ -Painlevé IV Equation

Nobutaka Nakazono

We consider a $q$ -Painlevé IV equation which is the $A_{4}^{(1)}$ -surface type in the Sakai's classification. We find three distinct types of classical solutions with determinantal s…

nlin.SI2009★ 18 cited

Projective reduction of the discrete Painlevé system of type $(A_{2} + A_{1})^{(1)}$

Kenji Kajiwara, Nobutaka Nakazono, Teruhisa Tsuda

We consider the q-Painlevé III equation arising from the birational representation of the affine Weyl group of type $(A_{2} + A_{1})^{(1)}$ . We study the reduction of the q-Painlevé II…

Special solutions to five autonomous integrable partial difference equations via the third and sixth Painlevé equations and the Garnier system in two variables

Solutions to an autonomous discrete KdV equation via Painlevé-type ordinary difference equations

A higher-order generalization of an A4(1)​-surface type q-Painlevé equation with W((A2N​⋊A1​)(1)×A1(1)​) symmetry

Higher-order generalizations of the A6(1)​- and A4(1)​-surface type q-Painlevé equations

Consistency around a cube property of Hirota's discrete KdV equation and the lattice sine-Gordon equation

Properties of the Non-Autonomous Lattice Sine-Gordon Equation: Consistency around a Broken Cube Property

Discrete Painlevé transcendent solutions to the multiplicative type discrete KdV equations

On the three-dimensional consistency of Hirota's discrete Korteweg-de Vries Equation

Reduction of quad-equations consistent around a cuboctahedron I: additive case

Discrete Power Functions on a Hexagonal Lattice I: Derivation of defining equations from the symmetry of the Garnier System in two variables

Classification of quad-equations on a cuboctahedron

A review of elliptic difference Painlevé equations

Geometric description of discrete power function associated with the sixth Painlevé equation

Reduction of lattice equations to the Painlevé equations: PIV​ and PV​

Elliptic Painlevé equations from next-nearest-neighbor translations on the E8(1)​ lattice

Reflection groups and discrete integrable systems

Lattice equations arising from discrete Painlevé systems. II. A4(1)​ case

Geometry of an elliptic-difference equation related to Q4

Lax pairs of discrete Painlevé equations: (A2​+A1​)(1) case

Lattice equations arising from discrete Painlevé systems (I): (A2​+A1​)(1) and (A1​+A1′​)(1) cases

A systematic approach to reductions of type-Q ABS equations

Hypergeometric solutions to the symmetric q-Painlevé equations

Hypergeometric Solutions of the A4(1)​-Surface q-Painlevé IV Equation

Projective reduction of the discrete Painlevé system of type (A2​+A1​)(1)

A higher-order generalization of an $A_{4}^{(1)}$ -surface type $q$ -Painlevé equation with $W ((A_{2 N} ⋊ A_{1})^{(1)} \times A_{1}^{(1)})$ symmetry

Higher-order generalizations of the $A_{6}^{(1)}$ - and $A_{4}^{(1)}$ -surface type $q$ -Painlevé equations

Reduction of lattice equations to the Painlevé equations: P $_{IV}$ and P $_{V}$

Elliptic Painlevé equations from next-nearest-neighbor translations on the $E_{8}^{(1)}$ lattice

Lattice equations arising from discrete Painlevé systems. II. $A_{4}^{(1)}$ case

Lax pairs of discrete Painlevé equations: $(A_{2} + A_{1})^{(1)}$ case

Lattice equations arising from discrete Painlevé systems (I): $(A_{2} + A_{1})^{(1)}$ and $(A_{1} + A_{1}^{'})^{(1)}$ cases

Hypergeometric Solutions of the $A_{4}^{(1)}$ -Surface $q$ -Painlevé IV Equation

Projective reduction of the discrete Painlevé system of type $(A_{2} + A_{1})^{(1)}$