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 $\tanh$-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 $G_4(N)$. 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 $G_4(N)$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