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Exactly Solvable and Integrable Systems papers — page 11

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Generating Quadrilateral and Circular Lattices in KP Theory
The bilinear equations of the N-component KP and BKP hierarchies and a corresponding extended Miwa transformation allow us to generate quadrilateral and circular lattices from conjugate and…
Adam Doliwa, Manuel Manas, Luis Martinez AlonsoOct 15, 1998
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Multiplicity Am Models
Models generalizing the su(2) XX spin-chain were recently introduced. These XXC models also have an underlying su(2) structure. Their construction method is shown to generalize to the chains based on…
Z. MaassaraniOct 15, 1998
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Pseudo-orthogonal groups and integrable dynamical systems in two dimensions
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and…
J. A. Calzada, M. A. del Olmo, M. A. RodriguezOct 14, 1998
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Fermionic flows and tau function of the N=(1|1) superconformal Toda lattice hierarchy
An infinite class of fermionic flows of the N=(1|1) superconformal Toda lattice hierarchy is constructed and their algebraic structure is studied. We completely solve the semi-infinite N=(1|1) Toda…
Olaf Lechtenfeld, Alexander SorinOct 13, 1998
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Quelques applications de l'Ansatz de Bethe (Some applications of the Bethe Ansatz)
The Bethe Ansatz is a method that is used in quantum integrable models in order to solve them explicitly. This method is explained here in a general framework, which applies to 1D quantum spin…
P. Zinn-JustinOct 11, 1998
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Classical Integrable 2-dim Models Inspired by SUSY Quantum Mechanics
A class of integrable 2-dim classical systems with integrals of motion of fourth order in momenta is obtained from the quantum analogues with the help of deformed SUSY algebra. With similar technique…
A. A. Andrianov, M. V. Ioffe, D. N. NishnianidzeOct 8, 1998
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Long range interaction corrections on the quantum vibronic soliton
Self-localized modes in a quantum vibronic system, with long range interaction of Kac-Baker type and interacting nonlinearly with an acoustical phonon bath, is studied. One works in the coherent…
D. Grecu, A. S. Cârstea, Anca VisinescuOct 7, 1998
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Zeros of the Jimbo, Miwa, Ueno tau function
We introduce a family of local deformations for meromorphic connections on the Riemann sphere in the neighborhood of a higher rank (simple) singularity. Following a scheme introduced by Malgrange we…
John PalmerOct 6, 1998
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Tau-function for discrete sine-Gordon equation and quantum R-matrix
We prove that the tau-function of the integrable discrete sine-Gordon model apart from the "standard" bilinar identities obeys a number of "non-standard" ones. They can be combined…
A. ZabrodinOct 1, 1998
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Integrable open boundary conditions for XXC models
The XXC models are multistate generalizations of the well known spin 1/2 XXZ model. These integrable models share a common underlying su(2) structure. We derive integrable open boundary conditions…
D. Arnaudon, Z. MaassaraniOct 1, 1998
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Generalized Jacobians of spectral curves and completely integrable systems
Consider an ordinary differential equation which has a Lax pair representation A'(x)= [A(x),B(x)], where A(x) is a matrix polynomial with a fixed regular leading coefficient and the matrix B(x)…
Lubomir GavrilovSep 30, 1998
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A Bilinear Approach to Discrete Miura Transformations
We present a systematic approach to the construction of Miura transformations for discrete Painlevé equations. Our method is based on the bilinear formalism and we start with the expression of the…
N. Joshi, A. Ramani, B. GrammaticosSep 24, 1998
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Lax Pairs for Integrable Lattice Systems
This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating…
R. S. WardSep 23, 1998
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The complex geometry of Lagrange top
We prove that the heavy symmetric top (Lagrange, 1788) linearizes on a two-dimensional non-compact algebraic group -- the generalized Jacobian of an elliptic curve with two points identified. This…
Lubomir Gavrilov, Angel ZhivkovSep 9, 1998
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The Generalised mKdV Equations for Level -3 of sl2
A certain generalisation of the hierarchy of mKdV equations (modified KdV), which forms an integrable system, is studied here. This generalisation is based on a Lax operator associated to the…
A. BalanSep 8, 1998
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Symmetries and exact solutions of some integrable Haldane-Shastry like spin chains
By using a class of `anyon like' representations of permutation algebra, which pick up nontrivial phase factors while interchanging the spins of two lattice sites, we construct some integrable…
B. Basu-MallickSep 3, 1998
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Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations
An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of first degree for systems of discrete evolution…
Wen-Xiu Ma, Benno FuchssteinerSep 3, 1998
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Linear r-Matrix Algebra for a Hierarchy of One-Dimensional Particle Systems Separable in Parabolic Coordinates
We consider a hierarchy of many-particle systems on the line with polynomial potentials separable in parabolic coordinates. The first non-trivial member of this hierarchy is a generalization of an…
J C Eilbeck, V Z Enol'skii, V B Kuznetsov et al.Sep 2, 1998
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A comparison of two discrete mKdV equations
We consider here two discrete versions of the modified KdV equation. In one case, some solitary wave solutions, Bäcklund transformations and integrals of motion are known. In the other one, only…
C. ChandreSep 1, 1998
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Osp(1|2) Off-shell Bethe Ansatz Equations
The semiclassical limit of the algebraic quantum inverse scattering method is used to solve the theory of the Gaudin model. Via Off-shell Bethe ansatz equations of an integrable representation of the…
A. Lima-SantosAug 31, 1998
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From 2D Integrable Systems to Self-Dual Gravity
We explain how to construct solutions to the self-dual Einstein vacuum equations from solutions of various two-dimensional integrable systems by exploiting the fact that the Lax formulations of both…
M. Dunajski, L. J. Mason, N. M. J. WoodhouseAug 31, 1998
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Elliptic Algebro-Geometric Solutions of the KdV and AKNS Hierarchies - An Analytic Approach
We provide an overview of elliptic algebro-geometric solutions of the KdV and AKNS hierarchies, with special emphasis on Floquet theoretic and spectral theoretic methods. Our treatment includes an…
Fritz Gesztesy, Rudi WeikardAug 31, 1998
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Algebro-Geometric Solutions of the Boussinesq Hierarchy
We continue a recently developed systematic approach to the Bousinesq (Bsq) hierarchy and its algebro-geometric solutions. Our formalism includes a recursive construction of Lax pairs and establishes…
Ronnie Dickson, Fritz Gesztesy, Karl UnterkoflerAug 31, 1998
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A Bethe ansatz solution for the closed Uq[sl(2)] Temperley-Lieb quantum spin chains
We solve the spectrum pf the closed Temperley-Lieb quantum spin chains using the coordinate Bethe ansatz. These Hamiltonians are invariante under the quantum group Uq[sl(2)]
A. Lima-Santos, R. C. T. GhiottoAug 31, 1998
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Bethe ansatz solution of a closed spin 1 XXZ Heisenberg chain with quantum algebra symmetry
A quantum algebra invariant integrable closed spin 1 chain is introduced and analysed in detail. The Bethe ansatz equations as well as the energy eigenvalues of the model are obtained. The highest…
Jon Links, Angela Foerster, Michael KarowskiAug 28, 1998
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