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Exactly Solvable and Integrable Systems papers — page 2

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Bicomplexes and finite Toda lattices
We associate bicomplexes with the finite Toda lattice and with a finite Toda field theory in such a way that conserved currents and charges are obtained by a simple iterative construction.
Aristophanes Dimakis, Folkert Muller-HoissenNov 16, 1999
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The KdV equation on a half-line
The initial boundary value problem on a half-line for the KdV equation with the boundary conditions u|x=0=a≤0, uxx|x=0=3a2 is integrated by means of the inverse scattering method. In…
I. T. Habibullin, A. N. Vil'danovNov 12, 1999
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A note on real forms of the complex N=4 supersymmetric Toda chain hierarchy in real N=2 and N=4 superspaces
Three inequivalent real forms of the complex N=4 supersymmetric Toda chain hierarchy (Nucl. Phys. B558 (1999) 545, solv-int/9907004) in the real N=2 superspace with one even and two odd real…
F. Delduc, A. SorinNov 4, 1999
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Integrable deformations of oscillator chains from quantum algebras
A family of completely integrable nonlinear deformations of systems of N harmonic oscillators are constructed from the non-standard quantum deformation of the sl(2,R) algebra. Explicit expressions…
Angel Ballesteros, Francisco J. HerranzNov 3, 1999
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Resonant Bifurcations
We consider dynamical systems depending on one or more real parameters, and assuming that, for some ``critical'' value of the parameters, the eigenvalues of the linear part are resonant, we…
Cicogna GNov 3, 1999
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Introduction to the functions on compact Riemann surfaces and theta-functions
We collect some classical results related to analysis on the Riemann surfaces. The notes may serve as an introduction to the field: we suppose that the reader is familiar only with the basic facts…
D. KorotkinNov 2, 1999
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Canonical transformations of the time for the Toda lattice and the Holt system
For the Toda lattice and the Holt system we consider properties of canonical transformations of the extended phase space, which preserve integrability. The separated variables are invariant under…
Andrey TsiganovOct 29, 1999
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The averaging of non-local Hamiltonian structures in Whitham's method
We consider the m-phase Whitham's averaging method and propose a procedure of "averaging" of non-local Hamiltonian structures. The procedure is based on the existence of a sufficient number of…
Andrei Ya. MaltsevOct 28, 1999
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Form factors of the SU(2) invariant massive Thirring model with boundary reflection
The SU(2) invariant massive Thirring model with a boundary is considered on the basis of the vertex operator approach. The bosonic formulae are presented for the vacuum vector and its dual in the…
H. Furutsu, T. Kojima, Y. -H. QuanoOct 28, 1999
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Schlesinger transformations for elliptic isomonodromic deformations
Schlesinger transformations are discrete monodromy preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these…
D. Korotkin, N. Manojlovic, H. SamtlebenOct 20, 1999
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N=2 Hamiltonians with sl(2) coalgebra symmetry and their integrable deformations
Two dimensional classical integrable systems and different integrable deformations for them are derived from phase space realizations of classical sl(2) Poisson coalgebras and their q-deformed…
A. Ballesteros, O. RagniscoOct 18, 1999
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Exact Solution of the Quantum Calogero-Gaudin System and of its q-Deformation
A complete set of commuting observables for the Calogero-Gaudin system is diagonalized, and the explicit form of the corresponding eigenvalues and eigenfunctions is derived. We use a purely algebraic…
F. Musso, O. RagniscoOct 18, 1999
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Singularity confinement and algebraic entropy: the case of the discrete Painlevé equations
We examine the validity of the results obtained with the singularity confinement integrability criterion in the case of discrete Painlevé equations. The method used is based on the requirement of…
Y. Ohta, K. M. Tamizhmani, B. Grammaticos et al.Oct 18, 1999
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Beyond Nonlinear Schrödinger Equation Approximation for an Anharmonic Chain with Harmonic Long Range Interaction
Multi scales method is used to analyze a nonlinear differential-difference equation. In order ε3 the NLS equation is found to determine the space-time evolution of the leading amplitude. In the…
D. Grecu, Anca Visinescu, A. S. CarsteaOct 15, 1999
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Lax pair, Darboux Transformations and solitonic solutions for a (2+1) dimensional NLSE
In this paper the Singular Manifold Method has allowed us to obtain the Lax pair, Darboux transformations and tau functions for a non-linear Schrödiger equation in 2+1 dimensions. In this way we can…
P. G. Estevez, G. A. HernáezOct 14, 1999
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On pulse broadening for optical solitons
Pulse broadening for optical solitons due to birefringence is investigated. We present an analytical solution which describes the propagation of solitons in birefringent optical fibers. The special…
H. J. S. Dorren, J. J. B. van den HeuvelOct 14, 1999
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On integrable discretization of the inhomogeneous Ablowitz-Ladik model
An integrable discretization of the inhomogeneous Ablowitz-Ladik model with a linear force is introduced. Conditions on parameters of the discretization which are necessary for reproducing Bloch…
V. V. KonotopOct 13, 1999
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Yang-Baxter Algebra for the n-Harmonic Oscillator Realisation of sp(2n,R)
Using a rational R-matrix associated with the 4 x 4 defining matrix representation of c2=sp(4), the Lie algebra of Sp(4), a one-site operator solution of the associated Yang-Baxter algebra acting in…
A. J. Macfarlane, F. WagnerOct 13, 1999
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Dispersionless Fermionic KdV
We analyze the dispersionless limits of the Kupershmidt equation, the SUSY KdV-B equation and the SUSY KdV equation. We present the Lax description for each of these models and bring out various…
J. Barcelos-Neto, Alin Constandache, Ashok DasOct 5, 1999
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Matrix integrals and the geometry of spinors
We obtain the collection of symmetric and symplectic matrix integrals and the collection of Pfaffian tau-functions, recently described by Peng and Adler and van Moerbeke, as specific elements in the…
Johan van de LeurSep 29, 1999
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Inter-relationships between orthogonal, unitary and symplectic matrix ensembles
We consider the following problem: When do alternate eigenvalues taken from a matrix ensemble themselves form a matrix ensemble? More precisely, we classify all weight functions for which alternate…
P. J. Forrester, E. M. RainsSep 29, 1999
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On two aspects of the Painleve analysis
We use the Calogero equation to illustrate the following two aspects of the Painleve analysis of nonlinear PDEs. First, if a nonlinear equation passes the Painleve test for integrability, the…
Sergei SakovichSep 26, 1999
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On a Schwarzian PDE associated with the KdV Hierarchy
We present a novel integrable non-autonomous partial differential equation of the Schwarzian type, i.e. invariant under Möbius transformations, that is related to the Korteweg-de Vries hierarchy. In…
Frank Nijhoff, Andrew Hone, Nalini JoshiSep 24, 1999
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Quasi-Lagrangian Systems of Newton Equations
Systems of Newton equations of the form q=-1/2A-1(q)∇ k with an integral of motion quadratic in velocities are studied. These equations generalize the potential case (when A=I, the…
Stefan Rauch-Wojciechowski, Krzysztof Marciniak, Hans LundmarkSep 22, 1999
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Dressing method and the coupled KP hierarchy
The coupled KP hierarchy, introduced by Hirota and Ohta, are investigated by using the dressing method. It is shown that the coupled KP hierarchy can be reformulated as a reduced case of the…
Saburo KakeiSep 22, 1999
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