48 research outputs found
Discrete localized modes supported by an inhomogeneous defocusing nonlinearity
We report that infinite and semi-infinite lattices with spatially
inhomogeneous self-defocusing (SDF)\ onsite nonlinearity, whose strength
increases rapidly enough toward the lattice periphery, support stable
unstaggered (UnST) discrete bright solitons, which do not exist in lattices
with the spatially uniform SDF nonlinearity. The UnST solitons coexist with
stable staggered (ST) localized modes, which are always possible under the
defocusing onsite nonlinearity. The results are obtained in a numerical form,
and also by means of variational approximation (VA). In the semi-infinite
(truncated) system, some solutions for the UnST surface solitons are produced
in an exact form. On the contrary to surface discrete solitons in uniform
truncated lattices, the threshold value of the norm vanishes for the UnST
solitons in the present system. Stability regions for the novel UnST solitons
are identified. The same results imply the existence of ST discrete solitons in
lattices with the spatially growing self-focusing nonlinearity, where such
solitons cannot exist either if the nonlinearity is homogeneous. In addition, a
lattice with the uniform onsite SDF nonlinearity and exponentially decaying
inter-site coupling is introduced and briefly considered too. Via a similar
mechanism, it may also support UnST discrete solitons, under the action of the
SDF nonlinearity. The results may be realized in arrayed optical waveguides and
collisionally inhomogeneous Bose-Einstein condensates trapped in deep optical
lattices. A generalization for a two-dimensional system is briefly considered
too.Comment: 14 pages, 7 figures, accepted for publication in PR
Interface solitons in one-dimensional locally-coupled lattice systems
Fundamental solitons pinned to the interface between two discrete lattices
coupled at a single site are investigated. Serially and parallel-coupled
identical chains (\textit{System 1} and \textit{System 2}), with the
self-attractive on-site cubic nonlinearity, are considered in one dimension. In
these two systems, which can be readily implemented as arrays of nonlinear
optical waveguides, symmetric, antisymmetric and asymmetric solitons are
investigated by means of the variational approximation (VA) and numerical
methods. The VA demonstrates that the antisymmetric solitons exist in the
entire parameter space, while the symmetric and asymmetric modes can be found
below some critical value of the coupling parameter. Numerical results confirm
these predictions for the symmetric and asymmetric fundamental modes. The
existence region of numerically found antisymmetric solitons is also limited by
a certain value of the coupling parameter. The symmetric solitons are
destabilized via a supercritical symmetry-breaking pitchfork bifurcation, which
gives rise to stable asymmetric solitons, in both systems. The antisymmetric
fundamental solitons, which may be stable or not, do not undergo any
bifurcation. In bistability regions stable antisymmetric solitons coexist with
either symmetric or asymmetric ones.Comment: 9 figure
Extreme Events in Nonlinear Lattices
The spatiotemporal complexity induced by perturbed initial excitations
through the development of modulational instability in nonlinear lattices with
or without disorder, may lead to the formation of very high amplitude,
localized transient structures that can be named as extreme events. We analyze
the statistics of the appearance of these collective events in two different
universal lattice models; a one-dimensional nonlinear model that interpolates
between the integrable Ablowitz-Ladik (AL) equation and the nonintegrable
discrete nonlinear Schr\"odinger (DNLS) equation, and a two-dimensional
disordered DNLS equation. In both cases, extreme events arise in the form of
discrete rogue waves as a result of nonlinear interaction and rapid coalescence
between mobile discrete breathers. In the former model, we find power-law
dependence of the wave amplitude distribution and significant probability for
the appearance of extreme events close to the integrable limit. In the latter
model, more importantly, we find a transition in the the return time
probability of extreme events from exponential to power-law regime. Weak
nonlinearity and moderate levels of disorder, corresponding to weak chaos
regime, favour the appearance of extreme events in that case.Comment: Invited Chapter in a Special Volume, World Scientific. 19 pages, 9
figure
Fundamental solitons in discrete lattices with a delayed nonlinear response
The formation of unstaggered localized modes in dynamical lattices can be
supported by the interplay of discreteness and nonlinearity with a finite
relaxation time. In rapidly responding nonlinear media, on-site discrete
solitons are stable, and their broad inter-site counterparts are marginally
stable, featuring a virtually vanishing real instability eigenvalue. The
solitons become unstable in the case of the slowly relaxing nonlinearity. The
character of the instability alters with the increase of the delay time, which
leads to a change in the dynamics of unstable discrete solitons. They form
robust localized breathers in rapidly relaxing media, and decay into
oscillatory diffractive pattern in the lattices with a slow nonlinear response.
Marginally stable solitons can freely move across the lattice.Comment: 8 figure
High- and low-frequency phonon modes in dipolar quantum gases trapped in deep lattices
We study normal modes propagating on top of the stable uniform background in
arrays of dipolar Bose-Einstein condensate (BEC) droplets trapped in a deep
optical lattice. Both the on-site mean-field dynamics of the droplets and their
displacement due to the repulsive dipole-dipole interactions (DDIs) are taken
into account. Dispersion relations for two modes, \textit{viz}., high- and low-
frequency counterparts of optical and acoustic phonon modes in condensed
matter, are derived analytically and verified by direct simulations, for both
cases of the repulsive and attractive contact interactions. The (counterpart of
the) optical-phonon branch does not exist without the DDIs. These results are
relevant in the connection to emerging experimental techniques enabling
real-time imaging of the condensate dynamics and direct experimental
measurement of phonon dispersion relations in BECs.Comment: Physical Review A, in pres
STATUS AND MEASURE FOR IMPROVE PASTURE CONDITIONS IN THE EASTERN PLANNING REGION OF MACEDONIA
The Eastern Planning Region occupies an area of 3548,7 km2 or 14,2% of the territory of the Republic of Macedonia. The region has 188.387 ha agricultural land. By that, the grasslands covers 119.504 ha, of which 110.640 ha under pastures and 8.864 ha under meadows, representing a significant source in the production of animal feed, especially in the mountainous areas of the region. On the other hand, on livestock unit comes 2,23 ha pasture area which shows that in this region livestock is poorly developed. As a consequence of this situation which from year to year deteriorates, pastures as a natural resource for providing feed degrade, reducing the quality of grass production and their economic value. In the absence of human factor as a corrector of the specific environmental conditions, hay production is relatively small, ranging from 300-600 kg-1ha-1. Considering the current situation, it is necessary to take certain agro-technical measures, such as introduction of methods of systematic grazing, overseeding, fertilization, weeds protection, etc., butalso introduced a system of organizational measures,as well a certain investments for larger agro and hydro technical operations how this status will be improved and agriculture but particularly livestock production become an important branch in economic development of this part of the country
Discrete solitons in an array of quantum dots
We develop a theory for the interaction of classical light fields with an a
chain of coupled quantum dots (QDs), in the strong-coupling regime, taking into
account the local-field effects. The QD chain is modeled by a one-dimensional
(1D) periodic array of two-level quantum particles with tunnel coupling between
adjacent ones. The local-field effect is taken into regard as QD depolarization
in the Hartree-Fock-Bogoliubov approximation. The dynamics of the chain is
described by a system of two discrete nonlinear Schr\"{o}dinger (DNLS)
equations for local amplitudes of the probabilities of the ground and first
excited states. The two equations are coupled by a cross-phase-modulation cubic
terms, produced by the local-field action, and by linear terms too. In
comparison with previously studied DNLS systems, an essentially new feature is
a phase shift between the intersite-hopping constants in the two equations. By
means of numerical solutions, we demonstrate that, in this QD chain, Rabi
oscillations (RO) self-trap into stable bright\textit{\ Rabi solitons} or
\textit{Rabi breathers}. Mobility of the solitons is considered too. The
related behavior of observable quantities, such as energy, inversion, and
electric-current density, is given a physical interpretation. The results apply
to a realistic region of physical parameters.Comment: 12 pages, 10 figures, Phys. Rev. B, in pres
High-speed kinks in a generalized discrete model
We consider a generalized discrete model and demonstrate that it can
support exact moving kink solutions in the form of tanh with an arbitrarily
large velocity. The constructed exact moving solutions are dependent on the
specific value of the propagation velocity. We demonstrate that in this class
of models, given a specific velocity, the problem of finding the exact moving
solution is integrable. Namely, this problem originally expressed as a
three-point map can be reduced to a two-point map, from which the exact moving
solutions can be derived iteratively. It was also found that these high-speed
kinks can be stable and robust against perturbations introduced in the initial
conditions.Comment: 10 pages, 5 figures, submitted to a journa