Dark soliton past a finite-size obstacle

We consider the collision of a dark soliton with an obstacle in a quasi-one-dimensional Bose condensate. We show that in many respects the soliton behaves as an effective classical particle of mass twice the mass of a bare particle, evolving in an effective potential which is a convolution of the actual potential describing the obstacle. Radiative effects beyond this approximation are also taken into account. The emitted waves are shown to form two counterpropagating wave packets, both moving at the speed of sound. We determine, at leading order, the total amount of radiation emitted during the collision and compute the acceleration of the soliton due to the collisional process. It is found that the radiative process is quenched when the velocity of the soliton reaches the velocity of sound in the system

Korteweg-de Vries description of Helmholtz-Kerr dark solitons

A wide variety of different physical systems can be described by a relatively small set of universal equations. For example, small-amplitude nonlinear Schrödinger dark solitons can be described by a Korteweg-de Vries (KdV) equation. Reductive perturbation theory, based on linear boosts and Gallilean transformations, is often employed to establish connections to and between such universal equations. Here, a novel analytical approach reveals that the evolution of small-amplitude Helmholtz–Kerr dark solitons is also governed by a KdV equation. This broadens the class of nonlinear systems that are known to possess KdV soliton solutions, and provides a framework for perturbative analyses when propagation angles are not negligibly small. The derivation of this KdV equation involves an element that appears new to weakly nonlinear analyses, since transformations are required to preserve the rotational symmetry inherent to Helmholtz-type equations

Lattice solitons in quasicondensates

We analyze finite temperature effects in the generation of bright solitons in condensates in optical lattices. We show that even in the presence of strong phase fluctuations solitonic structures with well defined phase profile can be created. We propose a novel family of variational functions which describe well the properties of these solitons and account for the non-linear effects in the band structure. We discuss also the mobility and collisions of these localized wave packets.Comment: 4 pages, 2 figure

Energy localization, Fano resonances, and nonlinear meta-optics

This paper reflects on some memories of the research topics developed at Department No. 29 of the Institute for Low Temperature Physics and Engineering in Kharkov more than 30 years ago. It also provides some recent advances on my major research activities related to those topics, including energy localization and solitons in nonlinear lattices, Fano resonances in photonics and phononics, and nonlinear effects in meta-optics and nanophotonics. Curiously enough, each of those topics can be associated with some memories and discussions that happened in Kharkov a long time ago

Two-color discrete localized modes and resonant scattering in arrays of nonlinear quadratic optical waveguides

We analyze the properties and stability of two-color discrete localized modes in arrays of channel waveguides where tunable quadratic nonlinearity is introduced as a nonlinear defect by periodic poling of a single waveguide in the array. We show that, depending on the value of the phase mismatch and the input power, such two-color defect modes can be realized in three different localized states. We also study resonant light scattering in the arrays with the defect waveguide.Comment: 10 pages, 3 figures, published in PR

Self-localization of a small number of Bose particles in a superfluid Fermi system

We consider self-localization of a small number of Bose particles immersed in a large homogeneous superfluid mixture of fermions in three and one dimensional spaces. Bosons distort the density of surrounding fermions and create a potential well where they can form a bound state analogous to a small polaron state. In the three dimensional volume we observe the self-localization for repulsive interactions between bosons and fermions. In the one dimensional case bosons self-localize as well as for attractive interactions forming, together with a pair of fermions at the bottom of the Fermi sea, a vector soliton. We analyze also thermal effects and show that small non-zero temperature affects the pairing function of the Fermi-subsystem and has little influence on the self-localization phenomena.Comment: 7 pages, 7 fiqures, improved versio

Optical solitons in PT\mathcal{PT}-symmetric nonlinear couplers with gain and loss

We study spatial and temporal solitons in the $\mathcal{PT}$ symmetric coupler with gain in one waveguide and loss in the other. Stability properties of the high- and low-frequency solitons are found to be completely determined by a single combination of the soliton's amplitude and the gain/loss coefficient of the waveguides. The unstable perturbations of the high-frequency soliton break the symmetry between its active and lossy components which results in a blowup of the soliton or a formation of a long-lived breather state. The unstable perturbations of the low-frequency soliton separate its two components in space blocking the power drainage of the active component and cutting the power supply to the lossy one. Eventually this also leads to the blowup or breathing.Comment: 14 pages, 11 figure