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

Proceedings of the Conference “Symmetries and Integrability of Difference Equations (SIDE-9)” (June 14–18, 2010, Varna, Bulgaria)

The Guest Editors for this special issue are

Boyka Aneva (Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria)
Vladimir Gerdjikov (Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria)
Plamen Iliev (Georgia Institute of Technology, Atlanta, USA)
Vassilis Papageorgiou (University of Patras, Greece)

The subject of difference equations stands at the frontier of pure and applied mathematics, and physics as well as theoretical biology. The theory of discrete equations related to integrability is an extremely rich field, related to algebra, analysis, complexity theory, “quantum geometry” (and quantum physics), algebraic geometry, and even number theory.

The present special issue of SIGMA contains papers closely related to the main themes of the conference “Symmetry, Integrability and Difference Equations (SIDE-9)” which took place at the International House of Scientists “Frederic Joliot-Curie” (IHS) on the Black Sea coast near Varna, Bulgaria, June 14–18, 2010.

SIDE-9 is the ninth in a series of biennial conferences devoted to Symmetries and Integrability of Difference Equations and related topics. These include ordinary and partial difference equations, analytic difference equations, orthogonal polynomials and special functions, symmetries and reductions, difference geometry, integrable discrete systems on graphs, integrable dynamical mappings, discrete Painlevé equations, singularity confinement, algebraic entropy, complexity and growth of multivalued mapping, representations of affine Weyl groups, quantum mappings and quantum field theory on the space-time lattice.

The conference was organized by Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences and the Institute of Informatics and Mathematics, Bulgarian Academy of Sciences. It was sponsored and supported by European Science Foundation, National Science Foundation of Bulgaria, European Physical Society, International Center for Theoretical Physics (Trieste), European Mathematical Society. It is our pleasure to thank the above-mentioned institutions for their support.

We refer to the conference web-page where one can find the list of participants, the titles and abstracts of their talks, and most of the presentations reported on the conference.

We would like also to thank all authors for their contributions to this issue, and all referees for providing helpful and constructive reviews.

Boyka L. Aneva, Vladimir S. Gerdjikov, Plamen Iliev, Vassilios G. Papageorgiou        

Papers in this Issue:

Families of Integrable Equations
Pavlos Kassotakis and Maciej Nieszporski
SIGMA 7 (2011), 100, 14 pages   [ abs   pdf ]
Symmetries of the Continuous and Discrete Krichever-Novikov Equation
Decio Levi, Pavel Winternitz and Ravil I. Yamilov
SIGMA 7 (2011), 097, 16 pages   [ abs   pdf ]
Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces
Vladimir S. Gerdjikov, Georgi G. Grahovski, Alexander V. Mikhailov and Tihomir I. Valchev
SIGMA 7 (2011), 096, 48 pages   [ abs   pdf ]
An Introduction to the q-Laguerre-Hahn Orthogonal q-Polynomials
Abdallah Ghressi, Lotfi Khériji and Mohamed Ihsen Tounsi
SIGMA 7 (2011), 092, 20 pages   [ abs   pdf ]
Symplectic Maps from Cluster Algebras
Allan P. Fordy and Andrew Hone
SIGMA 7 (2011), 091, 12 pages   [ abs   pdf ]
A Completeness Study on Certain 2×2 Lax Pairs Including Zero Terms
Mike C. Hay
SIGMA 7 (2011), 089, 12 pages   [ abs   pdf ]
Discrete-Time Goldfishing
Francesco Calogero
SIGMA 7 (2011), 082, 35 pages   [ abs   pdf ]
Linearizability of Nonlinear Equations on a Quad-Graph by a Point, Two Points and Generalized Hopf-Cole Transformations
Decio Levi and Christian Scimiterna
SIGMA 7 (2011), 079, 24 pages   [ abs   pdf ]
On Initial Data in the Problem of Consistency on Cubic Lattices for 3×3 Determinants
Oleg I. Mokhov
SIGMA 7 (2011), 075, 19 pages   [ abs   pdf ]
Singularities of Type-Q ABS Equations
James Atkinson
SIGMA 7 (2011), 073, 14 pages   [ abs   pdf ]
Soliton Taxonomy for a Modification of the Lattice Boussinesq Equation
Jarmo Hietarinta and Da-jun Zhang
SIGMA 7 (2011), 061, 14 pages   [ abs   pdf ]
Symmetries in Connection Preserving Deformations
Christopher M. Ormerod
SIGMA 7 (2011), 049, 16 pages   [ abs   pdf ]
Periodic and Solitary Wave Solutions of Two Component Zakharov-Yajima-Oikawa System, Using Madelung's Approach
Anca Visinescu, Dan Grecu, Renato Fedele and Sergio De Nicola
SIGMA 7 (2011), 041, 11 pages   [ abs   pdf ]
Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies
Mihai Visinescu
SIGMA 7 (2011), 037, 14 pages   [ abs   pdf ]

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