5 papers
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…
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…
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…
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 an…
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…