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The Guest Editors for this special issue are
Sergey Derkachov (St.Petersburg Department of Steklov Institute of Mathematics, Russia)
Tom Koornwinder (Universiteit van Amsterdam, the Netherlands)
Alexander Manashov (St.Petersburg State University, Russia)
Orlando Ragnisco (Universita di Roma Tre, Italy)
Evgueni Sklyanin (University of York, UK)
Andrey Tsiganov (St.Petersburg State University, Russia).
Dr Vadim B. Kuznetsov,
an expert in integrable systems, died on 16 December
2005, aged 42.
This issue includes papers from the fields in which Vadim worked:
separation of variables, classical and quantum integrable systems,
orthogonal polynomials and special functions, and other related fields.
The works presented here were mostly motivated by the research and organisational work
done by Vadim Kuznetsov.
Some of the papers have brief recollections of the meetings with
Vadim. See for instance the papers by
Aratyn & van de Leur, Grünbaum, Hone, Koornwinder, Langmann,
Loutsenko & Spiridonov, Mangazeev, Sinitsyn & Zhilinskii.
Please see the paper by his first adviser Igor V. Komarov for
Vadim's short biography and his list of publications.
The issue contains 56 papers with the total of 957 pages.
We would like to thank all the authors who have published papers in
the issue, and to give our special thanks to all the referees for
providing constructive reviews.
August 02, 2007
The Guest Editors
Papers in this Issue:
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Bäcklund Transformation for the BC-Type Toda Lattice
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Vadim Kuznetsov and Evgeny Sklyanin
SIGMA 3 (2007), 080, 17 pages [ abs
pdf ps ]
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Vadim Kuznetsov. Informal Biography by Eyes of His First Adviser
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Igor V. Komarov
SIGMA 3 (2007), 074, 6 pages [ abs
pdf ps ]
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Skew Divided Difference Operators and Schubert Polynomials
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Anatol N. Kirillov
SIGMA 3 (2007), 072, 14 pages [ abs
pdf ps ]
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Hamilton-Jacobi Theory and Moving Frames
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Joshua D. MacArthur, Raymond G. McLenaghan and Roman G. Smirnov
SIGMA 3 (2007), 070, 23 pages [ abs
pdf ps ]
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Yangian of the Strange Lie Superalgebra of Qn-1 Type, Drinfel'd Approach
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Vladimir Stukopin
SIGMA 3 (2007), 069, 12 pages [ abs
pdf ps ]
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Teichmüller Theory of Bordered Surfaces
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Leonid O. Chekhov
SIGMA 3 (2007), 066, 37 pages [ abs
pdf ps ]
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The Rahman Polynomials Are Bispectral
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F. Alberto Grünbaum
SIGMA 3 (2007), 065, 11 pages [ abs
pdf ps ]
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The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case
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Tom H. Koornwinder
SIGMA 3 (2007), 063, 15 pages [ abs
pdf ps ]
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Weakly Nonlocal Hamiltonian Structures: Lie Derivative and Compatibility
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Artur Sergyeyev
SIGMA 3 (2007), 062, 14 pages [ abs
pdf ps ]
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Completely Integrable Systems Associated with Classical Root Systems
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Toshio Oshima
SIGMA 3 (2007), 061, 50 pages [ abs
pdf ps ]
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Generating Operator of XXX or Gaudin Transfer Matrices Has Quasi-Exponential Kernel
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Evgeny Mukhin, Vitaly Tarasov and Alexander Varchenko
SIGMA 3 (2007), 060, 31 pages [ abs
pdf ps ]
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A Critical Phenomenon in Solitonic Ising Chains
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Igor M. Loutsenko and Vyacheslav P. Spiridonov
SIGMA 3 (2007), 059, 11 pages [ abs
pdf ps ]
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From su(2) Gaudin Models to Integrable Tops
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Matteo Petrera and Orlando Ragnisco
SIGMA 3 (2007), 058, 14 pages [ abs
pdf ps ]
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On the Applications of a New Technique to Solve Linear Differential Equations, with and without Source
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N. Gurappa, Pankaj K. Jha and Prasanta K. Panigrahi
SIGMA 3 (2007), 057, 6 pages [ abs
pdf ps ]
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Macdonald Polynomials and Multivariable Basic Hypergeometric Series
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Michael J. Schlosser
SIGMA 3 (2007), 056, 30 pages [ abs
pdf ps ]
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Bäcklund-Darboux Transformation for Non-Isospectral Canonical System and Riemann-Hilbert Problem
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Alexander Sakhnovich
SIGMA 3 (2007), 054, 11 pages [ abs
pdf ps ]
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Density of Eigenvalues of Random Normal Matrices with an Arbitrary Potential, and of Generalized Normal Matrices
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Pavel Etingof and Xiaoguang Ma
SIGMA 3 (2007), 048, 13 pages [ abs
pdf ps ]
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Qualitative Analysis of the Classical and Quantum Manakov Top
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Evguenii Sinitsyn and Boris Zhilinskii
SIGMA 3 (2007), 046, 23 pages [ abs
pdf ps ]
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Spectral Curves of Operators with Elliptic Coefficients
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J. Chris Eilbeck, Victor Z. Enolski and Emma Previato
SIGMA 3 (2007), 045, 17 pages [ abs
pdf ps ]
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A Discretization of the Nonholonomic Chaplygin Sphere Problem
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Yuri N. Fedorov
SIGMA 3 (2007), 044, 15 pages [ abs
pdf ps ]
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Hamiltonian Structure of PI Hierarchy
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Kanehisa Takasaki
SIGMA 3 (2007), 042, 32 pages [ abs
pdf ps ]
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Phase Space of Rolling Solutions of the Tippe Top
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S. Torkel Glad, Daniel Petersson and Stefan Rauch-Wojciechowski
SIGMA 3 (2007), 041, 14 pages [ abs
pdf ps ]
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q-Boson in Quantum Integrable Systems
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Anjan Kundu
SIGMA 3 (2007), 040, 14 pages [ abs
pdf ps ]
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N-Wave Equations with Orthogonal Algebras:
Z2 and Z2 × Z2 Reductions and Soliton Solutions
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Vladimir S. Gerdjikov, Nikolay A. Kostov and Tihomir I. Valchev
SIGMA 3 (2007), 039, 19 pages [ abs
pdf ps ]
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Towards Finite-Gap Integration of the Inozemtsev Model
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Kouichi Takemura
SIGMA 3 (2007), 038, 17 pages [ abs
pdf ps ]
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A 'User-Friendly' Approach to the Dynamical Equations of Non-Holonomic Systems
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Sergio Benenti
SIGMA 3 (2007), 036, 33 pages [ abs
pdf ps ]
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A Note on the Rotationally Symmetric SO(4) Euler Rigid Body
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Gregorio Falqui
SIGMA 3 (2007), 032, 13 pages [ abs
pdf ps ]
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Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones
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Edwin Langmann
SIGMA 3 (2007), 031, 18 pages [ abs
pdf ps ]
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The 6 Vertex Model and Schubert Polynomials
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Alain Lascoux
SIGMA 3 (2007), 029, 12 pages [ abs
pdf ps ]
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Bethe Ansatz for the Ruijsenaars Model of BC1-Type
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Oleg Chalykh
SIGMA 3 (2007), 028, 9 pages [ abs
pdf ps ]
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Quantum Super-Integrable Systems as Exactly Solvable Models
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Allan P. Fordy
SIGMA 3 (2007), 025, 10 pages [ abs
pdf ps ]
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Laurent Polynomials and Superintegrable Maps
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Andrew N.W. Hone
SIGMA 3 (2007), 022, 18 pages [ abs
pdf ps ]
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Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds
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Claudia Chanu and Giovanni Rastelli
SIGMA 3 (2007), 021, 21 pages [ abs
pdf ps ]
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Clifford Algebra Derivations of Tau-Functions for Two-Dimensional Integrable Models with Positive and Negative Flows
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Henrik Aratyn and Johan van de Leur
SIGMA 3 (2007), 020, 29 pages [ abs
pdf ps ]
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Separation of Variables and the Geometry of Jacobians
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Jacques Hurtubise
SIGMA 3 (2007), 017, 14 pages [ abs
pdf ps ]
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KP Trigonometric Solitons and an Adelic Flag Manifold
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Luc Haine
SIGMA 3 (2007), 015, 15 pages [ abs
pdf ps ]
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An Analytic Formula for the A2 Jack Polynomials
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Vladimir V. Mangazeev
SIGMA 3 (2007), 014, 11 pages [ abs
pdf ps ]
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Relativistic Toda Chain with Boundary Interaction at Root of Unity
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Nikolai Iorgov, Vladimir Roubtsov, Vitaly Shadura and Yuri Tykhyy
SIGMA 3 (2007), 013, 14 pages [ abs
pdf ps ]
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Asymmetric Twin Representation: the Transfer Matrix Symmetry
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Anastasia Doikou
SIGMA 3 (2007), 009, 19 pages [ abs
pdf ps ]
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Multi-Hamiltonian Structures on Beauville's Integrable System and Its Variant
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Rei Inoue and Yukiko Konishi
SIGMA 3 (2007), 007, 16 pages [ abs
pdf ps ]
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Symmetry Operators for the Fokker-Plank-Kolmogorov Equation with Nonlocal Quadratic Nonlinearity
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Alexander V. Shapovalov, Roman O. Rezaev and Andrey Yu. Trifonov
SIGMA 3 (2007), 005, 16 pages [ abs
pdf ps ]
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Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction
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Luc Vinet and Alexei Zhedanov
SIGMA 3 (2007), 003, 18 pages [ abs
pdf ps ]
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Raising and Lowering Operators for Askey-Wilson Polynomials
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Siddhartha Sahi
SIGMA 3 (2007), 002, 11 pages [ abs
pdf ps ]
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Invariant Varieties of Periodic Points for the Discrete Euler Top
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Satoru Saito and Noriko Saitoh
SIGMA 2 (2006), 098, 10 pages [ abs
pdf ps ]
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On the Darboux-Nijenhuis Variables for the Open Toda Lattice
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Yuriy A. Grigoryev and Andrey V. Tsiganov
SIGMA 2 (2006), 097, 15 pages [ abs
pdf ps ]
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Restricted Flows and the Soliton Equation with Self-Consistent Sources
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Runliang Lin, Haishen Yao and Yunbo Zeng
SIGMA 2 (2006), 096, 8 pages [ abs
pdf ps ]
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Bethe Ansatz Solutions of the Bose-Hubbard Dimer
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Jon Links and Katrina E. Hibberd
SIGMA 2 (2006), 095, 8 pages [ abs
pdf ps ]
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On the One Class of Hyperbolic Systems
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Vsevolod E. Adler and Alexey B. Shabat
SIGMA 2 (2006), 093, 17 pages [ abs
pdf ps ]
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A q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra
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Mark J. Hopkins and Alexander I. Molev
SIGMA 2 (2006), 092, 29 pages [ abs
pdf ps ]
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Solvable Nonlinear Evolution PDEs in Multidimensional Space
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Francesco Calogero and Matteo Sommacal
SIGMA 2 (2006), 088, 17 pages [ abs
pdf ps ]
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Multivariable Christoffel-Darboux Kernels and Characteristic Polynomials of Random Hermitian Matrices
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Hjalmar Rosengren
SIGMA 2 (2006), 085, 12 pages [ abs
pdf ps ]
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R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain
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Sergey É. Derkachov and Alexander N. Manashov
SIGMA 2 (2006), 084, 20 pages [ abs
pdf ps ]
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A Formula for the Logarithm of the KZ Associator
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Benjamin Enriquez and Fabio Gavarini
SIGMA 2 (2006), 080, 3 pages [ abs
pdf ps ]
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Coupled Modified KP Hierarchy and Its Dispersionless Limit
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Takashi Takebe and Lee-Peng Teo
SIGMA 2 (2006), 072, 30 pages [ abs
pdf ps ]
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Generalized Ellipsoidal and Sphero-Conal Harmonics
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Hans Volkmer
SIGMA 2 (2006), 071, 16 pages [ abs
pdf ps ]
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Integrable Models of Interaction of Matter with Radiation
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Vladimir I. Inozemtsev and Natalia G. Inozemtseva
SIGMA 2 (2006), 069, 9 pages [ abs
pdf ps ]
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