145 research outputs found
How to excite the internal modes of sine-Gordon solitons
We investigate the dynamics of the sine-Gordon solitons perturbed by
spatiotemporal external forces. We prove the existence of internal (shape)
modes of sine-Gordon solitons when they are in the presence of inhomogeneous
space-dependent external forces, provided some conditions (for these forces)
hold. Additional periodic time-dependent forces can sustain oscillations of the
soliton width. We show that, in some cases, the internal mode even can become
unstable, causing the soliton to decay in an antisoliton and two solitons. In
general, in the presence of spatiotemporal forces the soliton behaves as a
deformable (non-rigid) object. A soliton moving in an array of inhomogeneities
can also present sustained oscillations of its width. There are very important
phenomena (like the soliton-antisoliton collisions) where the existence of
internal modes plays a crucial role. We show that, under some conditions, the
dynamics of the soliton shape modes can be chaotic. A short report of some of
our results has been published in [J. A. Gonzalez et al., Phys. Rev. E, 65
(2002) 065601(R)].Comment: 14 .eps figures.To appear in Chaos, Solitons and Fractal
Spatiotemporal chaotic dynamics of solitons with internal structure in the presence of finite-width inhomogeneities
We present an analytical and numerical study of the Klein-Gordon kink-soliton
dynamics in inhomogeneous media. In particular, we study an external field that
is almost constant for the whole system but that changes its sign at the center
of coordinates and a localized impurity with finite-width. The soliton solution
of the Klein-Gordon-like equations is usually treated as a structureless
point-like particle. A richer dynamics is unveiled when the extended character
of the soliton is taken into account. We show that interesting spatiotemporal
phenomena appear when the structure of the soliton interacts with finite-width
inhomogeneities. We solve an inverse problem in order to have external
perturbations which are generic and topologically equivalent to well-known
bifurcation models and such that the stability problem can be solved exactly.
We also show the different quasiperiodic and chaotic motions the soliton
undergoes as a time-dependent force pumps energy into the traslational mode of
the kink and relate these dynamics with the excitation of the shape modes of
the soliton.Comment: 10 pages Revtex style article, 22 gziped postscript figures and 5 jpg
figure
Geometrical resonance in spatiotemporal systems
We generalize the concept of geometrical resonance to perturbed sine-Gordon,
Nonlinear Schrödinger and Complex Ginzburg-Landau equations. Using this
theory we can control different dynamical patterns. For instance, we can
stabilize breathers and oscillatory patterns of large amplitudes successfully
avoiding chaos. On the other hand, this method can be used to suppress
spatiotemporal chaos and turbulence in systems where these phenomena are
already present. This method can be generalized to even more general
spatiotemporal systems.Comment: 2 .epl files. Accepted for publication in Europhysics Letter
On the Bogomol'nyi bound in Einstein-Maxwell-dilaton gravity
It has been shown that the 4-dimensional Einstein-Maxwell-dilaton theory
allows a Bogomol'nyi-type inequality for an arbitrary dilaton coupling constant
, and that the bound is saturated if and only if the (asymptotically
flat) spacetime admits a nontrivial spinor satisfying the gravitino and the
dilatino Killing spinor equations. The present paper revisits this issue and
argues that the dilatino equation fails to ensure the dilaton field equation
unless the solution is purely electric/magnetic, or the dilaton coupling
constant is given by , corresponding to the
Brans-Dicke-Maxwell theory and the Kaluza-Klein reduction of 5-dimensional
vacuum gravity, respectively. A systematic classification of the supersymmetric
solutions reveals that the solution can be rotating if and only if the solution
is dyonic or the coupling constant is given by . This
implies that the theory with cannot be embedded into
supergravity except for the static truncation. Physical properties of
supersymmetric solutions are explored from various points of view.Comment: v2: 23 pages, typos corrected, minor modifications, to appear in CQ
Remarks on the Scalar Graviton Decoupling and Consistency of Horava Gravity
Recently Horava proposed a renormalizable gravity theory with higher
derivatives by abandoning the Lorenz invariance in UV. But there have been
confusions regarding the extra scalar graviton mode and the consistency of the
Horava model. I reconsider these problems and show that, in the Minkowski
vacuum background, the scalar graviton mode can be consistency decoupled from
the usual tensor graviton modes by imposing the (local) Hamiltonian as well as
the momentum constraints.Comment: Some clarifications regarding the projectable case added, Typos
corrected, Comments (Footnote No.9, Note Added) added, References updated,
Accepted in CQ
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