93 research outputs found
A direct method for solving the generalized sine-Gordon equation II
The generalized sine-Gordon (sG) equation
was derived as an integrable generalization of the sG equation. In a previous
paper (Matsuno Y 2010 J. Phys. A: Math. Theor. {\bf 43} 105204) which is
referred to as I, we developed a systematic method for solving the generalized
sG equation with . Here, we address the equation with . By
solving the equation analytically, we find that the structure of solutions
differs substantially from that of the former equation. In particular, we show
that the equation exhibits kink and breather solutions and does not admit
multi-valued solutions like loop solitons as obtained in I. We also demonstrate
that the equation reduces to the short pulse and sG equations in appropriate
scaling limits. The limiting forms of the multisoliton solutions are also
presented. Last, we provide a recipe for deriving an infinite number of
conservation laws by using a novel B\"acklund transformation connecting
solutions of the sG and generalized sG equations.Comment: To appear in J. Phys. A: Math. Theor. The first part of this paper
has been published in J. Phys. A: Math. Theor. 43 (2010) 10520
The Hyperbolic Heisenberg and Sigma Models in (1+1)-dimensions
Hyperbolic versions of the integrable (1+1)-dimensional Heisenberg
Ferromagnet and sigma models are discussed in the context of topological
solutions classifiable by an integer `winding number'. Some explicit solutions
are presented and the existence of certain classes of such winding solutions
examined.Comment: 13 pages, 1 figure, Latex, personal style file included tensind.sty,
Proof in section 3 altered, no changes to conclusion
Quantization of the N=2 Supersymmetric KdV Hierarchy
We continue the study of the quantization of supersymmetric integrable KdV
hierarchies. We consider the N=2 KdV model based on the affine
algebra but with a new algebraic construction for the L-operator, different
from the standard Drinfeld-Sokolov reduction. We construct the quantum
monodromy matrix satisfying a special version of the reflection equation and
show that in the classical limit, this object gives the monodromy matrix of N=2
supersymmetric KdV system. We also show that at both the classical and the
quantum levels, the trace of the monodromy matrix (transfer matrix) is
invariant under two supersymmetry transformations and the zero mode of the
associated U(1) current.Comment: LaTeX2e, 12 page
Quantum integrable multi atom matter-radiation models with and without rotating wave approximation
New integrable multi-atom matter-radiation models with and without rotating
wave approximation (RWA) are constructed and exactly solved through algebraic
Bethe ansatz. The models with RWA are generated through ancestor model approach
in an unified way. The rational case yields the standard type of
matter-radiaton models, while the trigonometric case corresponds to their
q-deformations. The models without RWA are obtained from the elliptic case at
the Gaudin and high spin limit.Comment: 9 pages, no figure, talk presented in int. conf. NEEDS04 (Gallipoli,
Italy, July 2004
The Zakharov-Shabat spectral problem on the semi-line: Hilbert formulation and applications
The inverse spectral transform for the Zakharov-Shabat equation on the
semi-line is reconsidered as a Hilbert problem. The boundary data induce an
essential singularity at large k to one of the basic solutions. Then solving
the inverse problem means solving a Hilbert problem with particular prescribed
behavior. It is demonstrated that the direct and inverse problems are solved in
a consistent way as soon as the spectral transform vanishes with 1/k at
infinity in the whole upper half plane (where it may possess single poles) and
is continuous and bounded on the real k-axis. The method is applied to
stimulated Raman scattering and sine-Gordon (light cone) for which it is
demonstrated that time evolution conserves the properties of the spectral
transform.Comment: LaTex file, 1 figure, submitted to J. Phys.
The Geometrodynamics of Sine-Gordon Solitons
The relationship between N-soliton solutions to the Euclidean sine-Gordon
equation and Lorentzian black holes in Jackiw-Teitelboim dilaton gravity is
investigated, with emphasis on the important role played by the dilaton in
determining the black hole geometry. We show how an N-soliton solution can be
used to construct ``sine-Gordon'' coordinates for a black hole of mass M, and
construct the transformation to more standard ``Schwarzchild-like''
coordinates. For N=1 and 2, we find explicit closed form solutions to the
dilaton equations of motion in soliton coordinates, and find the relationship
between the soliton parameters and the black hole mass. Remarkably, the black
hole mass is non-negative for arbitrary soliton parameters. In the one-soliton
case the coordinates are shown to cover smoothly a region containing the whole
interior of the black hole as well as a finite neighbourhood outside the
horizon. A Hamiltonian analysis is performed for slicings that approach the
soliton coordinates on the interior, and it is shown that there is no boundary
contribution from the interior. Finally we speculate on the sine-Gordon
solitonic origin of black hole statistical mechanics.Comment: Latex, uses epsf, 30 pages, 6 figures include
Factorization of the Universal R-matrix for
The factorization of the universal R-matrix corresponding to so called
Drinfeld Hopf structure is described on the example of quantum affine algebra
. As a result of factorization procedure we deduce certain
differential equations on the factors of the universal -matrix, which
allow to construct uniquely these factors in the integral form.Comment: 28 pages, LaTeX 2.09 using amssym.def and amssym.te
On the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions
The problem of calculation of correlation functions in the six-vertex model
with domain wall boundary conditions is addressed by considering a particular
nonlocal correlation function, called row configuration probability. This
correlation function can be used as building block for computing various (both
local and nonlocal) correlation functions in the model. The row configuration
probability is calculated using the quantum inverse scattering method; the
final result is given in terms of a multiple integral. The connection with the
emptiness formation probability, another nonlocal correlation function which
was computed elsewhere using similar methods, is also discussed.Comment: 15 pages, 2 figure
On elliptic solutions of the cubic complex one-dimensional Ginzburg-Landau equation
The cubic complex one-dimensional Ginzburg-Landau equation is considered.
Using the Hone's method, based on the use of the Laurent-series solutions and
the residue theorem, we have proved that this equation has neither elliptic
standing wave nor elliptic travelling wave solutions. This result amplifies the
Hone's result, that this equation has no elliptic travelling wave solutions.Comment: LaTeX, 12 page
Resolution of the Nested Hierarchy for Rational sl(n) Models
We construct Drinfel'd twists for the rational sl(n) XXX-model giving rise to
a completely symmetric representation of the monodromy matrix. We obtain a
polarization free representation of the pseudoparticle creation operators
figuring in the construction of the Bethe vectors within the framework of the
quantum inverse scattering method. This representation enables us to resolve
the hierarchy of the nested Bethe ansatz for the sl(n) invariant rational
Heisenberg model. Our results generalize the findings of Maillet and Sanchez de
Santos for sl(2) models.Comment: 25 pages, no figure
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