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Exactly Solvable and Integrable Systems papers — page 19

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Bispectral Operators, Dual Isomonodromic Deformations and the Riemann-Hilbert Dressing Method
A comparison is made between bispectral systems and dual isomonodromic deformation equations. A number of examples are given, showing how bispectral systems may be embedded into isomonodromic ones.…
J. HarnadOct 22, 1997
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Vectorial Ribaucour Transformations for the Lame Equations
The vectorial extension of the Ribaucour transformation for the Lame equations of orthogonal conjugates nets in multidimensions is given. We show that the composition of two vectorial Ribaucour…
Q. P. Liu, Manuel ManasOct 21, 1997
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Asymptotic dynamics of short-waves in nonlinear dispersive models
The multiple-scale perturbation theory, well known for long-waves, is extended to the study of the far-field behaviour of short-waves, commonly called ripples. It is proved that the…
M. A. Manna, V. MerleOct 20, 1997
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Hamiltonian Dynamics, Classical R-matrices and Isomonodromic Deformations
The Hamiltonian approach to the theory of dual isomonodromic deformations is developed within the framework of rational classical R-matrix structures on loop algebras. Particular solutions to the…
J. HarnadOct 18, 1997
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A Conjectured R-Matrix
A new spectral parameter independent R-matrix (that depends on all of the dynamical variables) is proposed for the elliptic Calogero-Moser models. Necessary and sufficient conditions for this…
H. W. BradenOct 17, 1997
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On Fifth Order KdV-Type Equation
The dynamics of the highly nonlinear fifth order KdV-type equation is discussed in the framework of the Lagrangian and Hamiltonian formalisms. The symmetries of the Lagrangian produce three…
R. P. MalikOct 16, 1997
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A new explicit expression for the Korteweg-De Vries hierarchy
We derive an improved fully explicit expression for the right-hand sides of the matrix KdV hierarchy using the relation to the heat kernel of the one-dimensional Schrödinger operator. Our method of…
Ivan G. Avramidi, Rainer SchimmingOct 16, 1997
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On classical string configurations
Equations which define classical configurations of strings in R3 are presented in a simple form. General properties as well as particular classes of solutions of these equations are considered.
B. G. Konopelchenko, G. LandolfiOct 15, 1997
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Equations of the reaction-diffusion type with a loop algebra structure
A system of equations of the reaction-diffusion type is studied in the framework of both the direct and the inverse prolongation structure. We find that this system allows an incomplete prolongation…
E. Alfinito, V. Grassi, R. A. Leo et al.Oct 13, 1997
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Binary Darboux-Backlund Transformations for the Manin-Radul Super KdV Hierarchy
We construct the supersymmetric extensions of the Darboux-Backlund transformations (DBTs) for the Manin-Radul super KdV hierarchy using the super-pseudo-differential operators. The elementary DBTs…
Jiin-Chang Shaw, Ming-Hsien TuOct 9, 1997
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AKS scheme for face and Calogero-Moser-Sutherland type models
We give the construction of quantum Lax equations for IRF models and difference versions of Calogero-Moser-Sutherland models introduced by Ruijsenaars. We solve the equations using factorization…
Branislav Jurco, Peter SchuppOct 9, 1997
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Two-body Elliptic Model in proper variables: Lie-algebraic forms and their discretizations
Two Lie algebraic forms of the 2-body Elliptic Calogero model are presented. Translation-invariant and dilatation-invariant discretizations of the model are obtained.
Alexander TurbinerOct 7, 1997
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Shock waves in one-dimensional Heisenberg ferromagnets
We use SU(2) coherent state path integral formulation with the stationary phase approximation to investigate, both analytically and numerically, the existence of shock waves in the one- dimensional…
V. V. Konotop, M. Salerno, S. TakenoOct 7, 1997
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Correlation functions for a strongly correlated boson system
The correlation functions for a strongly correlated exactly solvable one-dimensional boson system on a finite chain as well as in the thermodynamic limit are calculated explicitly. This system which…
N. M. Bogoliubov, A. G. Izergin, N. A. KitanineOct 6, 1997
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Susy Hierarchies and Affine Algebras
We review some basic features of the Lie-algebraic classification of W-algebras and related integrable hierarchies in 1+1 dimensions, pointing out the role of affine Lie algebras. We emphasize that…
Francesco ToppanOct 4, 1997
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On a two dimensional system associated with the complex of the solutions of the Tetrahedron equation
A sort of two dimensional linear auxiliary problem for the complex of 3D R -- operators associated with the Zamolodchikov -- Bazhanov -- Baxter statistical model is proposed. This problem resembles…
S. M. SergeevOct 2, 1997
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The Whitham Equations for Optical Communications: Mathematical Theory of NRZ
We present a model of optical communication system for high-bit-rate data transmission in the nonreturn-to-zero (NRZ) format over transoceanic distance. The system operates in a small group velocity…
Yuji KodamaSep 30, 1997
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Determinant Structure of the Rational Solutions for the Painlevé IV Equation
Rational solutions for the Painlevé IV equation are investigated by Hirota bilinear formalism. It is shown that the solutions in one hierarchy are expressed by 3-reduced Schur functions, and those in…
Kenji Kajiwara, Yasuhiro OhtaSep 29, 1997
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The Camassa-Holm Equation: A Loop Group Approach
A map is presented that associates with each element of a loop group a solution of an equation related by a simple change of coordinates to the Camassa-Holm (CH) Equation. Certain simple…
Jeremy SchiffSep 28, 1997
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Motion of Curves and Surfaces and Nonlinear Evolution Equations in (2+1) Dimensions
It is shown that a class of important integrable nonlinear evolution equations in (2+1) dimensions can be associated with the motion of space curves endowed with an extra spatial variable or…
M. Lakshmanan, R. Myrzakulov, S. Vijayalakshmi et al.Sep 20, 1997
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Nonlinear Physics: Integrability, Chaos and Beyond
Integrability and chaos are two of the main concepts associated with nonlinear physical systems which have revolutionized our understanding of them. Highly stable exponentially localized solitons are…
M. LakshmananSep 20, 1997
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Integrable discretizations for lattice systems: local equations of motion and their Hamiltonian properties
We develop the approach to the problem of integrable discretization based on the notion of r--matrix hierarchies. One of its basic features is the coincidence of Lax matrices of discretized systems…
Yuri B. SurisSep 18, 1997
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Discrete Levy Transformations and Casorati Determinant Solutions of Quadrilateral Lattices
Sequences of discrete Levy and adjoint Levy transformations for the multidimensional quadrilateral lattices are studied. After a suitable number of iterations we show how all the relevant geometrical…
Q. P. Liu, Manuel ManasSep 18, 1997
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Solutions of the functional tetrahedron equation connected with the local Yang -- Baxter equation for the ferro-electric
Local (or modified) Yang -- Baxter equation (LYBE) gives the functional map from the parameters of the weights in the left hand side to the parameters of the correspondent weights in the right hand…
S. M. SergeevSep 17, 1997
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Solitons from Dressing in an Algebraic Approach to the Constrained KP Hierarchy
The algebraic matrix hierarchy approach based on affine Lie sl (n) algebras leads to a variety of 1+1 soliton equations. By varying the rank of the underlying sl (n) algebra as well as its…
H. Aratyn, L. A. Ferreira, J. F. Gomes et al.Sep 11, 1997
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