67 research outputs found
Generalized Eikonal Knots and New Integrable Dynamical Systems
A new class of non-linear O(3) models is introduced. It is shown that these
systems lead to integrable submodels if an additional integrability condition
(so called the generalized eikonal equation) is imposed. In the case of
particular members of the family of the models the exact solutions describing
toroidal solitons with a non-trivial value of the Hopf index are obtained.
Moreover, the generalized eikonal equation is analyzed in detail. Topological
solutions describing torus knots are presented. Multi-knot configurations are
found as well.Comment: 13 page
Knots, Braids and Hedgehogs from the Eikonal Equation
The complex eikonal equation in the three space dimensions is considered. We
show that apart from the recently found torus knots this equation can also
generate other topological configurations with a non-trivial value of the
index: braided open strings as well as hedgehogs. In particular,
cylindric strings i.e. string solutions located on a cylinder with a constant
radius are found. Moreover, solutions describing strings lying on an arbitrary
surface topologically equivalent to cylinder are presented. We discus them in
the context of the eikonal knots. The physical importance of the results
originates in the fact that the eikonal knots have been recently used to
approximate the Faddeev-Niemi hopfions.Comment: 15 pages, 5 figure
Toroidal Solitons in Nicole-type Models
A family of modified Nicole models is introduced. We show that for particular
members of the family a topological soliton with a non-trivial value of the
Hopf index exists. The form of the solitons as well as their energy and
topological charge is explicitly found. They appear to be identical as the
so-called eikonal knots. The relation between energy and topological charge of
the solution is also presented. Quite interesting it seems to differ
drastically from the standard Vakulenko-Kapitansky formula.Comment: 9 pages, to be published in Eur. Phys. J.
Conservation laws in Skyrme-type models
The zero curvature representation of Zakharov and Shabat has been generalized
recently to higher dimensions and has been used to construct non-linear field
theories which either are integrable or contain integrable submodels. The
Skyrme model, for instance, contains an integrable subsector with infinitely
many conserved currents, and the simplest Skyrmion with baryon number one
belongs to this subsector. Here we use a related method, based on the geometry
of target space, to construct a whole class of theories which are either
integrable or contain integrable subsectors (where integrability means the
existence of infinitely many conservation laws). These models have
three-dimensional target space, like the Skyrme model, and their infinitely
many conserved currents turn out to be Noether currents of the
volume-preserving diffeomorphisms on target space. Specifically for the Skyrme
model, we find both a weak and a strong integrability condition, where the
conserved currents form a subset of the algebra of volume-preserving
diffeomorphisms in both cases, but this subset is a subalgebra only for the
weak integrable submodel.Comment: Latex file, 22 pages. Two (insignificant) errors in Eqs. 104-106
correcte
Investigation of restricted baby Skyrme models
A restriction of the baby Skyrme model consisting of the quartic and
potential terms only is investigated in detail for a wide range of potentials.
Further, its properties are compared with those of the corresponding full baby
Skyrme models. We find that topological (charge) as well as geometrical
(nucleus/shell shape) features of baby skyrmions are captured already by the
soliton solutions of the restricted model. Further, we find a coincidence
between the compact or non-compact nature of solitons in the restricted model,
on the one hand, and the existence or non-existence of multi-skyrmions in the
full baby Skyrme model, on the other hand.Comment: latex, 18 pages, 2 figures; some typos correcte
Investigation of the Nicole model
We study soliton solutions of the Nicole model - a non-linear
four-dimensional field theory consisting of the CP^1 Lagrangian density to the
non-integer power 3/2 - using an ansatz within toroidal coordinates, which is
indicated by the conformal symmetry of the static equations of motion. We
calculate the soliton energies numerically and find that they grow linearly
with the topological charge (Hopf index). Further we prove this behaviour to
hold exactly for the ansatz. On the other hand, for the full three-dimensional
system without symmetry reduction we prove a sub-linear upper bound,
analogously to the case of the Faddeev-Niemi model. It follows that symmetric
solitons cannot be true minimizers of the energy for sufficiently large Hopf
index, again in analogy to the Faddeev-Niemi model.Comment: Latex, 35 pages, 1 figur
A BPS Skyrme model and baryons at large Nc
Within the class of field theories with the field contents of the Skyrme
model, one submodel can be found which consists of the square of the baryon
current and a potential term only. For this submodel, a Bogomolny bound exists
and the static soliton solutions saturate this bound. Further, already on the
classical level, this BPS Skyrme model reproduces some features of the liquid
drop model of nuclei. Here, we investigate the model in more detail and,
besides, we perform the rigid rotor quantization of the simplest Skyrmion (the
nucleon). In addition, we discuss indications that the viability of the model
as a low energy effective field theory for QCD is further improved in the limit
of a large number of colors N_c.Comment: latex, 23 pages, 1 figure, a numerical error in section 3.2
corrected; matches published versio
Compact shell solitons in K field theories
Some models providing shell-shaped static solutions with compact support
(compactons) in 3+1 and 4+1 dimensions are introduced, and the corresponding
exact solutions are calculated analytically. These solutions turn out to be
topological solitons, and may be classified as maps and suspended
Hopf maps, respectively. The Lagrangian of these models is given by a scalar
field with a non-standard kinetic term (K field) coupled to a pure Skyrme term
restricted to , rised to the appropriate power to avoid the Derrick
scaling argument. Further, the existence of infinitely many exact shell
solitons is explained using the generalized integrability approach. Finally,
similar models allowing for non-topological compactons of the ball type in 3+1
dimensions are briefly discussed.Comment: 10 pages, latex, 2 figures, change in title and introduction.
Discussion section, 2 figures and references adde
Integrable subsystem of Yang--Mills dilaton theory
With the help of the Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2)
Yang-Mills field, we find an integrable subsystem of SU(2) Yang-Mills theory
coupled to the dilaton. Here integrability means the existence of infinitely
many symmetries and infinitely many conserved currents. Further, we construct
infinitely many static solutions of this integrable subsystem. These solutions
can be identified with certain limiting solutions of the full system, which
have been found previously in the context of numerical investigations of the
Yang-Mills dilaton theory. In addition, we derive a Bogomolny bound for the
integrable subsystem and show that our static solutions are, in fact, Bogomolny
solutions. This explains the linear growth of their energies with the
topological charge, which has been observed previously. Finally, we discuss
some generalisations.Comment: 25 pages, LaTex. Version 3: appendix added where the equivalence of
the field equations for the full model and the submodel is demonstrated;
references and some comments adde
Oscillons in gapless theories
We show that large scale oscillons, i.e., quasiperiodic, long-living particlelike solutions, may exist in massless theories, too. Their existence is explained using an effective (smeared) mass threshold which takesinto account nonlinear (finite) perturbations
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