33 research outputs found
Scattering of the double sine-Gordon kinks
We study the scattering of kink and antikink of the double sine-Gordon model.
There is a critical value of the initial velocity of the colliding
kinks, which separates different regimes of the collision. At
we observe kinks reflection, while at their interaction is
complicated with capture and escape windows. We obtain the dependence of
on the parameter of the model. This dependence possesses a series of
local maxima, which has not been reported by other authors. At some initial
velocities below the critical value we observe a new phenomenon -- the escape
of two oscillons in the final state. Besides that, at we found
the initial kinks' velocities at which the oscillons do not escape, and the
final configuration looks like a bound state of two oscillons.Comment: 12 pages, 7 figures; v2: minor changes to match version published in
EPJ
Multi-kink collisions in the model
We study simultaneous collisions of two, three, and four kinks and antikinks
of the model at the same spatial point. Unlike the kinks, the
kinks are asymmetric and this enriches the variety of the collision
scenarios. In our numerical simulations we observe both reflection and bound
state formation depending on the number of kinks and on their spatial ordering
in the initial configuration. We also analyze the extreme values of the energy
densities and the field gradient observed during the collisions. Our results
suggest that very high energy densities can be produced in multi-kink
collisions in a controllable manner. Appearance of high energy density spots in
multi-kink collisions can be important in various physical applications of the
Klein-Gordon model.Comment: 21 pages, 8 figures; v2: minor changes to match version published in
JHE
Multi-kink scattering in the double sine-Gordon model
We study collisions of two, three, and four kinks of the double sine-Gordon
model. The initial conditions are taken in a special form in order to provide
collision of all kinks in one point. We obtain dependences of the maximal
energy densities on the model parameter. We also analyze the final states
observed in these collisions.Comment: 24 pages, 12 figures; v2: figures, discussion and references added;
matches the published versio
Discrete breathers assist energy transfer to ac driven nonlinear chains
One-dimensional chain of pointwise particles harmonically coupled with
nearest neighbors and placed in six-order polynomial on-site potentials is
considered. Power of the energy source in the form of single ac driven
particles is calculated numerically for different amplitudes and
frequencies within the linear phonon band. The results for the on-site
potentials with hard and soft nonlinearity types are compared. For the
hard-type nonlinearity, it is shown that when the driving frequency is close to
(far from) the {\em upper} edge of the phonon band, the power of the energy
source normalized to increases (decreases) with increasing . In
contrast, for the soft-type nonlinearity, the normalized power of the energy
source increases (decreases) with increasing when the driving frequency is
close to (far from) the {\em lower} edge of the phonon band. Our further
demonstrations indicate that, in the case of hard (soft) anharmonicity, the
chain can support movable discrete breathers (DBs) with frequencies above
(below) the phonon band. It is the energy source quasi-periodically emitting
moving DBs in the regime with driving frequency close to the DBs frequency,
that induces the increase of the power. Therefore, our results here support the
mechanism that the moving DBs can assist energy transfer from the ac driven
particle to the chain.Comment: 11 pages, 13 figure
Interaction of Sine-Gordon Kinks and Breathers With a Parity-Time-Symmetric Defect
The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized parity-time-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy, and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. The kink phase shift and critical velocity are calculated by means of the collective variable method. Kink-kink (kink-antikink) collisions at the defect are also briefly considered, showing how their pairwise repulsive (respectively, attractive) interaction can modify the collisional outcome of a single kink within the pair with the defect. For the breather, the result of its interaction with the defect depends strongly on the breather parameters (velocity, frequency, and initial phase) and on the defect parameters. The breather can gain some energy from the defect and as a result potentially even split into a kink-antikink pair, or it can lose a part of its energy. Interestingly, the breather translational mode is very weakly affected by the dissipative perturbation, so that a breather penetrates more easily through the defect when it comes from the lossy side, than a kink. In all studied soliton-defect interactions, the energy loss to radiation of small-amplitude extended waves is negligible
Soliton-potential interaction in the nonlinear Klein-Gordon model
The interaction of solitons with external potentials in nonlinear
Klein-Gordon field theory is investigated using an improved model. The
presented model has been constructed with a better approximation for adding the
potential to the Lagrangian through the metric of background space-time. The
results of the model are compared with another model and the differences are
discussed.Comment: 14 pages,8 figure
Collective-coordinate analysis of inhomogeneous nonlinear Klein-Gordon field theory
Two different sets of collective-coordinate equations for solitary solutions
of Nonlinear Klein-Gordon (NKG) model is introduced. The collective-coordinate
equations are derived using different approaches for adding the inhomogeneities
as exrernal potentials to the soliton equation of motion. Interaction of the
NKG field with a local inhomogeneity like a delta function potential wall and
also delta function potential well is investigated using the presented
collective-coordinate equations and the results of two different models are
compared. Most of the characters of the interaction are derived analytically.
Analytical results are also compared with the results of numerical simulations.Comment: 16 pages, 8 figures. Accepted for publication in Volume 43 of the
Brazilian Journal of Physic