
Special Issue on Symmetries and Integrability of Difference Equations
The Guest Editors for this special issue are
Véronique Hussin (Université de Montréal, Canada)
Mourad Ismail (University of Central Florida, USA)
Decio Levi (Università degli Studi Roma Tre, Italy)
Zora Thomova (SUNY Polytechnic Institute, USA)
Pavel Winternitz (Université de Montréal, Canada)
Topics for this Special Issue will include:
 discrete, continuous and ultradiscrete Painlevé equations;
 orthogonal polynomials, special functions and their relation to discrete integrable systems and their elliptic analogs;
 integrability criteria for single and multivariable difference equations and differential difference equations;
 discrete differential geometry;
 discrete integrable systems and isomonodromy transformations;
 Yang–Baxter maps and quantum discrete integrable systems;
 continuous symmetries of discrete equations;
 structure preserving discretization of differential equations and numerical methods;
 cluster algebras and discrete integrable systems;
 dynamics on graphs and combinatorics;
 difference Galois theory;
 lattices and symmetries in physical applications.
The special issue is related to SIDE12 conference which was held at Le Chantecler, in SteAdèle, Québec, Canada (the Laurentian area near Montréal), from July 4, 2016 to July 9, 2016, under the same name as the proposed title of the issue.
Participants in the conference SIDE12 and others whose work is concerned with the above topics, in particular participants in earlier SIDE meetings, are invited
to submit papers to the special issue.
How to Submit an Article to the Issue.
For this issue both original research articles and review papers (not published or considered for publication elsewhere) are welcome and will be refereed according to the
usual standards of SIGMA.
There is no limit to the length of an article. Deadline for paper submission is May 01, 2017.
Papers in this Issue:

Darboux Integrability of Trapezoidal $H^{4}$ and $H^{6}$ Families of Lattice Equations II: General Solutions

Giorgio Gubbiotti, Christian Scimiterna and Ravil I. Yamilov
SIGMA 14 (2018), 008, 51 pages [ abs
pdf ]

Reconstructing a Lattice Equation: a NonAutonomous Approach to the Hietarinta Equation

Giorgio Gubbiotti and Christian Scimiterna
SIGMA 14 (2018), 004, 21 pages [ abs
pdf ]

Rational Solutions to the ABS List: Transformation Approach

Danda Zhang and DaJun Zhang
SIGMA 13 (2017), 078, 24 pages [ abs
pdf ]

Coherent Transport in Photonic Lattices: A Survey of Recent Analytic Results

ÉricOlivier Bossé and Luc Vinet
SIGMA 13 (2017), 074, 19 pages [ abs
pdf ]

Classification of a Subclass of TwoDimensional Lattices via Characteristic Lie Rings

Ismagil Habibullin and Mariya Poptsova
SIGMA 13 (2017), 073, 26 pages [ abs
pdf ]

$N$BrightDark Soliton Solution to a SemiDiscrete Vector Nonlinear Schrödinger Equation

BaoFeng Feng and Yasuhiro Ohta
SIGMA 13 (2017), 071, 16 pages [ abs
pdf ]

Rational Solutions of the PainlevéII Equation Revisited

Peter D. Miller and Yue Sheng
SIGMA 13 (2017), 065, 29 pages [ abs
pdf ]

Relativistic DNLS and KaupNewell Hierarchy

Oktay K. Pashaev and JyhHao Lee
SIGMA 13 (2017), 058, 13 pages [ abs
pdf ]

On Reductions of the HirotaMiwa Equation

Andrew N.W. Hone, Theodoros E. Kouloukas and Chloe Ward
SIGMA 13 (2017), 057, 17 pages [ abs
pdf ]

Symmetries of the Hirota Difference Equation

Andrei K. Pogrebkov
SIGMA 13 (2017), 053, 14 pages [ abs
pdf ]

SelfDual Systems, their Symmetries and Reductions to the Bogoyavlensky Lattice

Allan P. Fordy and Pavlos Xenitidis
SIGMA 13 (2017), 051, 10 pages [ abs
pdf ]

MultiPoisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation

Hayato Chiba
SIGMA 13 (2017), 025, 27 pages [ abs
pdf ]

