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Exactly Solvable and Integrable Systems papers — page 20

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Matched Pulse Propagation in a Three-Level System
The Bäcklund transformation for the three-level Maxwell-Bloch equation is presented in the matrix potential formalism. By applying the Bäcklund transformation to a constant electric field background,…
Q-Han Park, H. J. ShinSep 2, 1997
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Field Theory for Coherent Optical Pulse Propagation
We introduce a new notion of "matrix potential" to nonlinear optical systems. In terms of a matrix potential g, we present a gauge field theoretic formulation of the Maxwell-Bloch equation…
Q-Han Park, H. J. ShinSep 2, 1997
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Separation of variables via integral transformations
For a system of linear partial differential equations (LPDEs) we introduce an operator equation for auxiliary operators. These operators are used to construct a kernel of an integral transformation…
Ya. V. Lisitsyn, A. V. ShapovalovSep 2, 1997
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Pure quantum integrability
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system…
Jarmo HietarintaAug 28, 1997
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d=2, N=2 Superconformally Covariant Operators and Super W-Algebras
We construct and classify superconformally covariant differential operators defined on N=2 super Riemann surfaces. By contrast to the N=1 theory, these operators give rise to partial rather than…
F. Gieres, S. GourmelenAug 22, 1997
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Nonlocal extended conformal algebras associated with multi-constraint KP hierarchy and their free-field realizations
We study the conformal properties of the multi-constraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures…
Jiin-Chang Shaw, Ming-Hsien TuAug 20, 1997
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Generating function of correlators in the sl2 Gaudin model
For the sl2 Gaudin model (degenerated quantum integrable XXX spin chain) an exponential generating function of correlators is calculated explicitely. The calculation relies on the Gauss…
E. K. SklyaninAug 18, 1997
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Introduction to the Hirota bilinear method
We give an elementary introduction to Hirota's direct method of constructing multisoliton solutions to integrable nonlinear evolution equations. We discuss in detail how this works for equations…
J. HietarintaAug 14, 1997
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On the Integrable Hierarchies Associated With N=2 Super Wn Algebra
A new Lax operator is proposed from the viewpoint of constructing the integrable hierarchies related with N=2 super Wn algebra. It is shown that the Poisson algebra associated to the second…
Q. P. LiuAug 14, 1997
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Criterion and Regions of Stability for Quasi-Equidistant Soliton Trains
Using the complex Toda chain (CTC) as a model for the propagation of the N-soliton pulse trains of the nonlinear Schrodinger (NLS) equation, we predict the asymptotic behavior of these trains. The…
V. S. Gerdjikov, E. G. Evstatiev, D. J. Kaup et al.Aug 14, 1997
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Three Graded Modified Classical Yang-Baxter Equations and Integrable Systems
The 6 = 3× 2 huge Lie algebra Ξ of all local and non local differential operators on a circle is applied to the standard Adler-Kostant-Symes (AKS) R-bracket sckeme. It is shown in particular…
E. H. Saidi, M. B. SedraAug 11, 1997
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Nonstandard Drinfeld-Sokolov reduction
Subject to some conditions, the input data for the Drinfeld-Sokolov construction of KdV type hierarchies is a quadruplet (,Λ, d1, d0), where the di are -gradations of a loop algebra …
F. Delduc, L. Feher, L. GallotAug 7, 1997
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Two-dimensional soliton cellular automaton of deautonomized Toda-type
A deautonomized version of the two-dimensional Toda lattice equation is presented. Its ultra-discrete analogue and soliton solutions are also discussed.
A. Nagai, T. Tokihiro, J. Satsuma et al.Aug 4, 1997
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Bihamiltonian Reductions and Wn Algebras
We discuss the geometry of the Marsden-Ratiu reduction theorem for a bihamiltonian manifold. We consider the case of the manifolds associated with the Gel'fand-Dickey theory, i.e., loop algebras…
Paolo Casati, Gregorio Falqui, Franco Magri et al.Jul 29, 1997
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Continuum limit of nonlinear discrete systems with long range interaction potentials
One dimensional nonlinear lattices with harmonic long range interaction potentials (LRIP) having an inverse power kernel type, are studied. For the nearest neighbour nonlinear interaction we consider…
A. S. Cârstea, D. Grecu, A. VisinescuJul 29, 1997
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The constrained modified KP hierarchy and the generalized Miura transformations
In this letter, we consider the second Hamiltonian structure of the constrained modified KP hierarchy. After mapping the Lax operator to a pure differential operator the second structure becomes the…
Jiin-Chang Shaw, Ming-Hsien TuJul 27, 1997
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Bifurcation diagram of a one-parameter family of dispersive waves
The Korteweg de Vries (KdV) equation with small dispersion is a model for the formation and propagation of dispersive shock waves in one dimension. Dispersive shock waves in KdV are characterized by…
T. GravaJul 24, 1997
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Algebra of non-local charges in the O(N) WZNW model at and beyond criticality
We derive the classical algebra of the non-local conserved charges in the O(N) WZNW model and analyze its dependence on the coupling constant of the Wess-Zumino term. As in the non-linear sigma…
L. E. Saltini, A. ZadraJul 24, 1997
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The Constrained MKP Hierarchy and the Generalized Kupershmidt-Wilson Theorem
The constrained Modified KP hierarchy is considered from the viewpoint of modification. It is shown that its second Poisson bracket, which has a rather complicated form, is associated to a vastly…
Q. P. LiuJul 24, 1997
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A combined sine-Gordon and modified Korteweg-de Vries hierarchy and its algebro-geometric solutions
We derive a zero-curvature formalism for a combined sine-Gordon (sG) and modified Korteweg-de Vries (mKdV) equation which yields a local sGmKdV hierarchy. In complete analogy to other completely…
Fritz Gesztesy, Helge HoldenJul 20, 1997
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An Alternative Approach to Algebro-Geometric Solutions of the AKNS Hierarchy
We develop an alternative systematic approach to the AKNS hierarchy based on elementary algebraic methods. In particular, we recursively construct Lax pairs for the entire AKNS hierarchy by…
Fritz Gesztesy, Ratnam RatnaseelanJul 14, 1997
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Functional representation of the Ablowitz-Ladik hierarchy
The Ablowitz-Ladik hierarchy (ALH) is considered in the framework of the inverse scattering approach. After establishing the structure of solutions of the auxiliary linear problems, the ALH, which…
V. E. VekslerchikJul 14, 1997
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On Density of State of Quantized Willmore Surface-A Way to Quantized Extrinsic String in R3
Recently I quantized an elastica with Bernoulli-Euler functional in two-dimensional space using the modified KdV hierarchy. In this article, I will quantize a Willmore surface, or equivalently a…
Shigeki MatsutaniJul 10, 1997
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Quantum Coupled Nonlinear Schrödinger System with Different Masses
In this letter, I have considered one-dimensional quantum system with different masses m and M, which does not appear integrable in general. However I have found an exact two-body wave function…
Shigeki MatsutaniJul 9, 1997
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Solvability of the G2 Integrable System
It is shown that the 3-body trigonometric G2 integrable system is exactly-solvable. If the configuration space is parametrized by certain symmetric functions of the coordinates then, for arbitrary…
Marcos Rosenbaum, Alexander Turbiner, Antonio CapellaJul 7, 1997
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