57 research outputs found
Einstein-Infeld-Hoffman method and soliton dynamics in a parity noninvariant system
We consider slow motion of a pointlike topological defect (vortex) in the
nonlinear Schrodinger equation minimally coupled to Chern-Simons gauge field
and subject to external uniform magnetic field. It turns out that a formal
expansion of fields in powers of defect velocity yields only the trivial static
solution. To obtain a nontrivial solution one has to treat velocities and
accelerations as being of the same order. We assume that acceleration is a
linear form of velocity. The field equations linearized in velocity uniquely
determine the linear relation. It turns out that the only nontrivial solution
is the cyclotron motion of the vortex together with the whole condensate. This
solution is a perturbative approximation to the center of mass motion known
from the theory of magnetic translations.Comment: 6 pages in Latex; shortened version to appear in Phys.Rev.
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
Travelling solitons in the parametrically driven nonlinear Schroedinger equation
We show that the parametrically driven nonlinear Schroedinger equation has
wide classes of travelling soliton solutions, some of which are stable. For
small driving strengths nonpropogating and moving solitons co-exist while
strongly forced solitons can only be stably when moving sufficiently fast.Comment: The paper is available as the JINR preprint E17-2000-147(Dubna,
Russia) and the preprint of the Max-Planck Institute for the Complex Systems
mpipks/0009011, Dresden, Germany. It was submitted to Physical Review
Existence threshold for the ac-driven damped nonlinear Schr\"odinger solitons
It has been known for some time that solitons of the externally driven,
damped nonlinear Schr\"odinger equation can only exist if the driver's
strength, , exceeds approximately , where is the
dissipation coefficient. Although this perturbative result was expected to be
correct only to the leading order in , recent studies have demonstrated
that the formula gives a remarkably accurate
description of the soliton's existence threshold prompting suggestions that it
is, in fact, exact. In this note we evaluate the next order in the expansion of
showing that the actual reason for this phenomenon is simply
that the next-order coefficient is anomalously small: . Our approach is based on a singular perturbation expansion
of the soliton near the turning point; it allows to evaluate
to all orders in and can be easily reformulated for other perturbed
soliton equations.Comment: 8 pages in RevTeX; 5 figures in ps format included in the text. To be
published in Physica
Solitons in polarized double layer quantum Hall systems
A new manifestation of interlayer coherence in strongly polarized double
layer quantum Hall systems with total filling factor
in the presence of a small or zero tunneling is theoretically
predicted. It is shown that moving (for small tunneling) and spatially
localized (for zero tunneling) stable pseudospin solitons develop which could
be interpreted as mobile or static charge-density excitations.
The possibility of their experimental observation is also discussed.Comment: Phys. Rev. B (accepted
Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation
It is well known that pulse-like solutions of the cubic complex
Ginzburg-Landau equation are unstable but can be stabilised by the addition of
quintic terms. In this paper we explore an alternative mechanism where the role
of the stabilising agent is played by the parametric driver. Our analysis is
based on the numerical continuation of solutions in one of the parameters of
the Ginzburg-Landau equation (the diffusion coefficient ), starting from the
nonlinear Schr\"odinger limit (for which ). The continuation generates,
recursively, a sequence of coexisting stable solutions with increasing number
of humps. The sequence "converges" to a long pulse which can be interpreted as
a bound state of two fronts with opposite polarities.Comment: 13 pages, 6 figures; to appear in PR
Pattern formation and localization in the forced-damped FPU lattice
We study spatial pattern formation and energy localization in the dynamics of
an anharmonic chain with quadratic and quartic intersite potential subject to
an optical, sinusoidally oscillating field and a weak damping. The
zone-boundary mode is stable and locked to the driving field below a critical
forcing that we determine analytically using an approximate model which
describes mode interactions. Above such a forcing, a standing modulated wave
forms for driving frequencies below the band-edge, while a ``multibreather''
state develops at higher frequencies. Of the former, we give an explicit
approximate analytical expression which compares well with numerical data. At
higher forcing space-time chaotic patterns are observed.Comment: submitted to Phys.Rev.
Semiclassical Quantization for the Spherically Symmetric Systems under an Aharonov-Bohm magnetic flux
The semiclassical quantization rule is derived for a system with a
spherically symmetric potential and an
Aharonov-Bohm magnetic flux. Numerical results are presented and compared with
known results for models with . It is shown that the
results provided by our method are in good agreement with previous results. One
expects that the semiclassical quantization rule shown in this paper will
provide a good approximation for all principle quantum number even the rule is
derived in the large principal quantum number limit . We also discuss
the power parameter dependence of the energy spectra pattern in this
paper.Comment: 13 pages, 4 figures, some typos correcte
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