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Exactly Solvable and Integrable Systems papers — page 4

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Complete integrability of derivative nonlinear Schrödinger-type equations
We study matrix generalizations of derivative nonlinear Schrödinger-type equations, which were shown by Olver and Sokolov to possess a higher symmetry. We prove that two of them are…
Takayuki Tsuchida, Miki WadatiAug 11, 1999
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A Coupled AKNS-Kaup-Newell Soliton Hierarchy
A coupled AKNS-Kaup-Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and…
Wen-Xiu Ma, Ruguang ZhouAug 9, 1999
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Integrable ODEs on Associative Algebras
In this paper we give definitions of basic concepts such as symmetries, first integrals, Hamiltonian and recursion operators suitable for ordinary differential equations on associative algebras, and…
A. V. Mikhailov, V. V. SokolovAug 6, 1999
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Classical Solutions Generating Tree Form-Factors in Yang-Mills, Sin(h)-Gordon and Gravity
Classical solutions generating tree form-factors are defined and constructed in various models.
K. G. SelivanovAug 1, 1999
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Non-additive fusion, Hubbard models and non-locality
In the framework of quantum groups and additive R-matrices, the fusion procedure allows to construct higher-dimensional solutions of the Yang-Baxter equation. These solutions lead to integrable…
Z. MaassaraniJul 31, 1999
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Quantum Backlund transformation for the integrable DST model
For the integrable case of the discrete self-trapping (DST) model we construct a Backlund transformation. The dual Lax matrix and the corresponding dual Backlund transformation are also found and…
V. B. Kuznetsov, M. Salerno, E. K. SklyaninJul 31, 1999
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Supersymmetric KP hierarchy in N=1 superspace and its N=2 reductions
A wide class of N=2 reductions of the supersymmetric KP hierarchy in N=1 superspace is described. This class includes a new N=2 supersymmetric generalization of the Toda chain hierarchy. The Lax pair…
Olaf Lechtenfeld, Alexander SorinJul 29, 1999
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Soliton Cellular Automata Associated With Crystal Bases
We introduce a class of cellular automata associated with crystals of irreducible finite dimensional representations of quantum affine algebras U'q(n). They have solitons labeled by…
Goro Hatayama, Atsuo Kuniba, Taichiro TakagiJul 27, 1999
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Miura Map between Lattice KP and its Modification is Canonical
We consider the Miura map between the lattice KP hierarchy and the lattice modified KP hierarchy and prove that the map is canonical not only between the first Hamiltonian structures, but also…
Q. P. LiuJul 22, 1999
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Multi-Field Integrable Systems Related to WKI-Type Eigenvalue Problems
Higher flows of the Heisenberg ferromagnet equation and the Wadati-Konno-Ichikawa equation are generalized into multi-component systems on the basis of the Lax formulation. It is shown that there is…
Takayuki Tsuchida, Miki WadatiJul 22, 1999
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A Spectral Mapping Theorem and Invariant Manifolds for Nonlinear Schrödinger Equations
A spectral mapping theorem is proved that resolves a key problem in applying invariant manifold theorems to nonlinear Schr\" odinger type equations. The theorem is applied to the operator that…
F. Gesztesy, C. K. R. T. Jones, Y. Latushkin et al.Jul 17, 1999
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Symmetric Linear Backlund Transformation for Discrete BKP and DKP equation
Proper lattices for the discrete BKP and the discrete DKP equaitons are determined. Linear Bäcklund transformation equations for the discrete BKP and the DKP equations are constructed, which…
Nobuhiko ShinzawaJul 15, 1999
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Discrete Dubrovin Equations and Separation of Variables for Discrete Systems
A universal system of difference equations associated with a hyperelliptic curve is derived constituting the discrete analogue of the Dubrovin equations arising in the theory of finite-gap…
F. W. NijhoffJul 15, 1999
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The symmetric, D-invariant and Egorov reductions of the quadrilateral lattice
We present a detailed study of the geometric and algebraic properties of the multidimensional quadrilateral lattice (a lattice whose elementary quadrilaterals are planar; the discrete analogue of a…
Adam Doliwa, Paolo Maria SantiniJul 8, 1999
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Integrable Discrete Geometry: the Quadrilateral Lattice, its Transformations and Reductions
We review recent results on Integrable Discrete Geometry. It turns out that most of the known (continuous and/or discrete) integrable systems are particular symmetries of the quadrilateral lattice, a…
Adam Doliwa, Paolo Maria SantiniJul 8, 1999
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Lattice geometry of the Hirota equation
Geometric interpretation of the Hirota equation is presented as equation describing the Laplace sequence of two-dimensional quadrilateral lattices. Different forms of the equation are given together…
Adam DoliwaJul 8, 1999
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Spectral decomposition for the Dirac system associated to the DSII equation
A new (scalar) spectral decomposition is found for the Dirac system in two dimensions associated to the focusing Davey--Stewartson II (DSII) equation. Discrete spectrum in the spectral problem…
Dmitry E. Pelinovsky, Catherine SulemJul 8, 1999
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A construction for R-matrices without difference property in the spectral parameter
A new construction is given for obtaining R-matrices which solve the McGuire-Yang-Baxter equation in such a way that the spectral parameters do not possess the difference property. A discussion of…
Jon LinksJul 8, 1999
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Integrable Systems in the Infinite Genus Limit
We provide an elementary approach to integrable systems associated with hyperelliptic curves of infinite genus. In particular, we explore the extent to which the classical Burchnall-Chaundy theory…
Fritz GesztesyJul 7, 1999
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New Integrable Coupled Nonlinear Schrodinger Equations
Two types of integrable coupled nonlinear Schrodinger (NLS) equations are derived by using Zakharov-Shabat (ZS) dressing method.The Lax pairs for the coupled NLS equations are also investigated using…
Hendry I. ElimJul 2, 1999
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Integrable supersymmetric correlated electron chain with open boundaries
We construct an extended Hubbard model with open boundaries from a R-matrix based on the Uq[Osp(2|2)] superalgebra. We study the reflection equation and find two classes of diagonal solutions.…
M. J. Martins, X. W. GuanJul 2, 1999
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On A Recently Proposed Relation Between oHS and Ito Systems
The bi-Hamiltonian structure of original Hirota-Satsuma system proposed by Roy based on a modification of the bi-Hamiltonian structure of Ito system is incorrect.
Atalay KarasuJun 30, 1999
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N=2 local and N=4 nonlocal reductions of supersymmetric KP hierarchy in N=2 superspace
A N=4 supersymmetric matrix KP hierarchy is proposed and a wide class of its reductions which are characterized by a finite number of fields are described. This class includes the one-dimensional…
F. Delduc, L. Gallot, A. SorinJun 29, 1999
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A New Class of Optical Solitons
Existence of a new class of soliton solutions is shown for higher order nonlinear Schrodinger equation, describing thrid order dispersion, Kerr effect and stimulated Raman scattering. These new…
Sasanka Ghosh, Sudipta NandyJun 28, 1999
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On the equivalence of the discrete nonlinear Schrödinger equation and the discrete isotropic Heisenberg magnet
The equivalence of the discrete isotropic Heisenberg magnet (IHM) model and the discrete nonlinear Schrödinger equation (NLSE) given by Ablowitz and Ladik is shown. This is used to derive the…
Tim HoffmannJun 28, 1999
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