Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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 Non-Autonomous 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 Da-Jun Zhang
SIGMA 13 (2017), 078, 24 pages   [ abs   pdf ]
Coherent Transport in Photonic Lattices: A Survey of Recent Analytic Results
Éric-Olivier Bossé and Luc Vinet
SIGMA 13 (2017), 074, 19 pages   [ abs   pdf ]
Classification of a Subclass of Two-Dimensional Lattices via Characteristic Lie Rings
Ismagil Habibullin and Mariya Poptsova
SIGMA 13 (2017), 073, 26 pages   [ abs   pdf ]
$N$-Bright-Dark Soliton Solution to a Semi-Discrete Vector Nonlinear Schrödinger Equation
Bao-Feng Feng and Yasuhiro Ohta
SIGMA 13 (2017), 071, 16 pages   [ abs   pdf ]
Rational Solutions of the Painlevé-II Equation Revisited
Peter D. Miller and Yue Sheng
SIGMA 13 (2017), 065, 29 pages   [ abs   pdf ]
Relativistic DNLS and Kaup-Newell Hierarchy
Oktay K. Pashaev and Jyh-Hao Lee
SIGMA 13 (2017), 058, 13 pages   [ abs   pdf ]
On Reductions of the Hirota-Miwa 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 ]
Self-Dual Systems, their Symmetries and Reductions to the Bogoyavlensky Lattice
Allan P. Fordy and Pavlos Xenitidis
SIGMA 13 (2017), 051, 10 pages   [ abs   pdf ]
Multi-Poisson Approach to the Painlevé Equations: from the Isospectral Deformation to the Isomonodromic Deformation
Hayato Chiba
SIGMA 13 (2017), 025, 27 pages   [ abs   pdf ]

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