93 research outputs found
Exact vortex solutions of the complex sine-Gordon theory on the plane
We construct explicit multivortex solutions for the first and second complex
sine-Gordon equations. The constructed solutions are expressible in terms of
the modified Bessel and rational functions, respectively. The vorticity-raising
and lowering Backlund transformations are interpreted as the Schlesinger
transformations of the fifth Painleve equation.Comment: 10 pages, 1 figur
Duality in Complex sine-Gordon Theory
New aspects of the complex sine-Gordon theory are addressed through the
reformulation of the theory in terms of the gauged Wess-Zumino-Witten action. A
dual transformation between the theory for the coupling constant \b > 0 and
the theory for \b < 0 is given which agrees with the Krammers-Wannier duality
in the context of perturbed conformal field theory. The B\"{a}cklund transform
and the nonlinear superposition rule for the complex sine-Gordon theory are
presented and from which, exact solutions, solitons and breathers with U(1)
charge, are derived. We clarify topological and nontopological nature of
neutral and charged solitons respectively, and discuss about the duality
between the vector and the axial U(1) charges.Comment: 10 pages, LaTe
Dyonic Giant Magnons
We study the classical spectrum of string theory on AdS_5 X S^5 in the
Hofman-Maldacena limit. We find a family of classical solutions corresponding
to Giant Magnons with two independent angular momenta on S^5. These solutions
are related via Pohlmeyer's reduction procedure to the charged solitons of the
Complex sine-Gordon equation. The corresponding string states are dual to BPS
boundstates of many magnons in the spin-chain description of planar N=4 SUSY
Yang-Mills. The exact dispersion relation for these states is obtained from a
purely classical calculation in string theory.Comment: LaTeX file, 16 pages. One figure. Corrected reference
Noncoaxial multivortices in the complex sine-Gordon theory on the plane
We construct explicit multivortex solutions for the complex sine-Gordon
equation (the Lund-Regge model) in two Euclidean dimensions. Unlike the
previously found (coaxial) multivortices, the new solutions comprise single
vortices placed at arbitrary positions (but confined within a finite part of
the plane.) All multivortices, including the single vortex, have an infinite
number of parameters. We also show that, in contrast to the coaxial complex
sine-Gordon multivortices, the axially-symmetric solutions of the
Ginzburg-Landau model (the stationary Gross-Pitaevskii equation) {\it do not}
belong to a broader family of noncoaxial multivortex configurations.Comment: 40 pages, 7 figures in colou
Локальные и сплайновые аппроксимации в цифровой обработке геомагнитных наблюдений
Methods of local and spline approximations for digital processing of geomagnetic observations are proposed for consideration. Algorithms for calculating piecewise-linear, sinusoidal and pol-ynomial local approximation models have been developed. An algorithm for calculating the spline approximation model is developed. The generated mathematical apparatus is focused on solving problems of parameter estimation, filtering and spectral analysis for geomagnetic observations.Предлагаются к рассмотрению методы локальных и сплайновых аппроксимаций для цифровой обработки геомагнитных наблюдений. Разработаны алгоритмы вычислений кусочно- линейных, синусоидальных и полиномиальных локальных аппроксимационных моделей. Разработан алгоритм вычисления сплайновой аппроксимационной модели. Сформированный математический аппарат ориентирован на решения задач оценивания параметров, фильтрации и спектрального анализа для геомагнитных наблюдений
Massive Integrable Soliton Theories
Massive integrable field theories in dimensions are defined at the
Lagrangian level, whose classical equations of motion are related to the
``non-abelian'' Toda field equations. They can be thought of as generalizations
of the sine-Gordon and complex sine-Gordon theories. The fields of the theories
take values in a non-abelian Lie group and it is argued that the coupling
constant is quantized, unlike the situation in the sine-Gordon theory, which is
a special case since its field takes values in an abelian group. It is further
shown that these theories correspond to perturbations of certain coset
conformal field theories. The solitons in the theories will, in general, carry
non-abelian charges.Comment: 18 pages, no figures, plain tex with macro include
Quantum scattering of charged solitons in the complex sine-Gordon model
The scattering of charged solitons in the complex sine-Gordon field theory is
investigated. An exact factorizable S-matrix for the theory is proposed when
the renormalized coupling constant takes the values
for any integer : the minimal S-matrix associated with the Lie algebra
. It is shown that the proposed S-matrix reproduces the leading
semiclassical behaviour of all amplitudes in the theory and is the minimal
S-matrix which is consistent with the semiclassical spectrum of the model. The
results are completely consistent with the description of the complex
sine-Gordon theory as the SU coset model at level perturbed
by its first thermal operator.Comment: SWAT-4
Magnons, their Solitonic Avatars and the Pohlmeyer Reduction
We study the solitons of the symmetric space sine-Gordon theories that arise
once the Pohlmeyer reduction has been imposed on a sigma model with the
symmetric space as target. Under this map the solitons arise as giant magnons
that are relevant to string theory in the context of the AdS/CFT
correspondence. In particular, we consider the cases S^n, CP^n and SU(n) in
some detail. We clarify the construction of the charges carried by the solitons
and also address the possible Lagrangian formulations of the symmetric space
sine-Gordon theories. We show that the dressing, or Backlund, transformation
naturally produces solitons directly in both the sigma model and the symmetric
space sine-Gordon equations without the need to explicitly map from one to the
other. In particular, we obtain a new magnon solution in CP^3. We show that the
dressing method does not produce the more general "dyonic" solutions which
involve non-trivial motion of the collective coordinates carried by the
solitons.Comment: 52 page
The complex Sine-Gordon equation as a symmetry flow of the AKNS Hierarchy
It is shown how the complex sine-Gordon equation arises as a symmetry flow of
the AKNS hierarchy. The AKNS hierarchy is extended by the ``negative'' symmetry
flows forming the Borel loop algebra. The complex sine-Gordon and the vector
Nonlinear Schrodinger equations appear as lowest negative and second positive
flows within the extended hierarchy. This is fully analogous to the well-known
connection between the sine-Gordon and mKdV equations within the extended mKdV
hierarchy.
A general formalism for a Toda-like symmetry occupying the ``negative''
sector of sl(N) constrained KP hierarchy and giving rise to the negative Borel
sl(N) loop algebra is indicated.Comment: 8 pages, LaTeX, typos corrected, references update
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