400 research outputs found
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
Some Comments on BPS systems
We look at simple BPS systems involving more than one field. We discuss the
conditions that have to be imposed on various terms in Lagrangians involving
many fields to produce BPS systems and then look in more detail at the simplest
of such cases. We analyse in detail BPS systems involving 2 interacting
Sine-Gordon like fields, both when one of them has a kink solution and the
second one either a kink or an antikink solution. We take their solitonic
static solutions and use them as initial conditions for their evolution in
Lorentz covariant versions of such models. We send these structures towards
themselves and find that when they interact weakly they can pass through each
other with a phase shift which is related to the strength of their interaction.
When they interact strongly they repel and reflect on each other. We use the
method of a modified gradient flow in order to visualize the solutions in the
space of fields.Comment: 27 pages, 17 figure
Scaling, self-similar solutions and shock waves for V-shaped field potentials
We investigate a (1+1)-dimensional nonlinear field theoretic model with the
field potential It can be obtained as the universal small
amplitude limit in a class of models with potentials which are symmetrically
V-shaped at their minima, or as a continuum limit of certain mechanical system
with infinite number of degrees of freedom. The model has an interesting
scaling symmetry of the 'on shell' type. We find self-similar as well as shock
wave solutions of the field equation in that model.Comment: Two comments and one reference adde
Scattering of compact oscillons
We study various aspects of the scattering of generalized compact oscillons in the signum-Gordon model in (1+1) dimensions. Using covariance of the model we construct traveling oscillons and study their interactions and the dependence of these interactions on the oscillons’ initial velocities and their relative phases. The scattering processes transform the two incoming oscillons into two outgoing ones and lead to the generation of extra oscillons which appear in the form of jet-like cascades. Such cascades vanish for some values of free parameters and the scattering processes, even though our model is non-integrable, resemble typical scattering processes normally observed for integrable or quasi-integrable models. Occasionally, in the intermediate stage of the process, we have seen the emission of shock waves and we have noticed that, in general, outgoing oscillons have been more involved in their emission than the initial ones i.e. they have a border in the form of curved worldlines. The results of our studies of the scattering of oscillons suggest that the radiation of the signum-Gordon model has a fractal-like nature
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