439 research outputs found
Stability of localized modes in PT-symmetric nonlinear potentials
We report on detailed investigation of the stability of localized modes in
the nonlinear Schrodinger equations with a nonlinear parity-time (alias PT)
symmetric potential. We are particularly focusing on the case where the
spatially-dependent nonlinearity is purely imaginary. We compute the Evans
function of the linear operator determining the linear stability of localized
modes. Results of the Evans function analysis predict that for sufficiently
small dissipation localized modes become stable when the propagation constant
exceeds certain threshold value. This is the case for periodic and
-shaped complex potentials where the modes having widths comparable with
or smaller than the characteristic width of the complex potential are stable,
while broad modes are unstable. In contrast, in complex potentials that change
linearly with transverse coordinate all modes are stable, what suggests that
the relation between width of the modes and spatial size of the complex
potential define the stability in the general case. These results were
confirmed using the direct propagation of the solutions for the mentioned
examples.Comment: 6 pages, 4 figures; accepted to Europhysics Letters,
https://www.epletters.net
Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media
We review the latest progress and properties of the families of bright and
dark one-dimensional periodic waves propagating in saturable Kerr-type and
quadratic nonlinear media. We show how saturation of the nonlinear response
results in appearance of stability (instability) bands in focusing (defocusing)
medium, which is in sharp contrast with the properties of periodic waves in
Kerr media. One of the key results discovered is the stabilization of
multicolor periodic waves in quadratic media. In particular, dark-type waves
are shown to be metastable, while bright-type waves are completely stable in a
broad range of energy flows and material parameters. This yields the first
known example of completely stable periodic wave patterns propagating in
conservative uniform media supporting bright solitons. Such results open the
way to the experimental observation of the corresponding self-sustained
periodic wave patterns.Comment: 29 pages, 10 figure
Dynamics of surface solitons at the edge of chirped optical lattices
We address soliton formation at the edge of chirped optical lattices
imprinted in Kerr-type nonlinear media. We find families of power thresholdless
surface waves that do not exist at other types of lattice interfaces. Such
solitons form due to combined action of internal reflection at the interface,
distributed Bragg-type reflection, and focusing nonlinearity. Remarkably, we
discover that surfaces of chirped lattices are soliton attractors: Below an
energy threshold, solitons launched well within the lattice self-bend toward
the interface, and then stick to it.Comment: 13 pages, 4 figure
Structurally parametric identification of object descrete models with delay for tuning smith controllers
Construction of Smith digital controller on the basis of equivalence principle of dynamic object models with delay has been suggeste
Three-dimensional spatiotemporal optical solitons in nonlocal nonlinear media
We demonstrate the existence of stable three-dimensional spatiotemporal
solitons (STSs) in media with a nonlocal cubic nonlinearity. Fundamental
(nonspinning) STSs forming one-parameter families are stable if their
propagation constant exceeds a certain critical value, that is inversely
proportional to the range of nonlocality of nonlinear response. All spinning
three-dimensional STSs are found to be unstable.Comment: 14 pages, 6 figures, accepted to PRE, Rapid Communication
Nonlinear optics and light localization in periodic photonic lattices
We review the recent developments in the field of photonic lattices
emphasizing their unique properties for controlling linear and nonlinear
propagation of light. We draw some important links between optical lattices and
photonic crystals pointing towards practical applications in optical
communications and computing, beam shaping, and bio-sensing.Comment: to appear in Journal of Nonlinear Optical Physics & Materials (JNOPM
Soliton topology versus discrete symmetry in optical lattices
We address the existence of vortex solitons supported by azimuthally
modulated lattices and reveal how the global lattice discrete symmetry has
fundamental implications on the possible topological charges of solitons. We
set a general ``charge rule'' using group-theory techniques, which holds for
all lattices belonging to a given symmetry group. Focusing in the case of
Bessel lattices allows us to derive also a overall stability rule for the
allowed vortex solitons.Comment: 4 pages, 3 figures. To appear in Phys. Rev. Let
Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions
All non-equivalent solutions of vacuum Maxwell equations are found for the
case when space-time manifolds admit simply transitive four-parameter groups of
motions . The potentials of the admissible electromagnetic fields admit
the existence of the algebra of motion integrals of the Hamilton-Jacobi and
Klein-Gordon-Fock equations which is isomorphic to the algebra of the group
operators for the same group Comment: 15 pages, will be published in Journal of Geometric Methods in Modern
Physic
Stable spatiotemporal solitons in Bessel optical lattices
We investigate the existence and stability of three-dimensional (3D) solitons
supported by cylindrical Bessel lattices (BLs) in self-focusing media. If the
lattice strength exceeds a threshold value, we show numerically, and using the
variational approximation, that the solitons are stable within one or two
intervals of values of their norm. In the latter case, the Hamiltonian-vs.-norm
diagram has a "swallowtail" shape, with three cuspidal points. The model
applies to Bose-Einstein condensates (BECs) and to optical media with saturable
nonlinearity, suggesting new ways of making stable 3D BEC solitons and "light
bullets" of an arbitrary size.Comment: 9 pages, 4 figures, Phys. Rev. Lett., in pres
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