Valeriy A. Brazhnyi

Nonlocal gap solitons in PT -symmetric periodic potentials with defocusing nonlinearity

Existence and stability of

Solitary waves in coupled nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities

mathcal{PT}

Localization and delocalization of two-dimensional discrete solitons pinned to linear and nonlinear defects

-symmetric gap solitons in a periodic structure with defocusing nonlocal nonlinearity are studied both theoretically and numerically. We find that, for any degree of nonlocality, gap solitons are always unstable in the presence of an imaginary potential. The instability manifests itself as a lateral drift of solitons due to an unbalanced particle flux. We also demonstrate that the perturbation growth rate is proportional to the amount of gain (loss), thus predicting the observability of stable gap solitons for small imaginary potentials.

Stable multidimensional soliton stripes in two-component Bose–Einstein condensates

Abstract Using Lie group theory we construct explicit solitary wave solutions of coupled nonlinear Schrodinger systems with spatially inhomogeneous nonlinearities. We present the general theory, use it to construct different families of explicit solutions and study their linear and dynamical stability.

Solitons in dipolar Bose–Einstein condensates with a trap and barrier potential

We study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schrödinger equation, including a local linear or nonlinear defect. Discrete solitons pinned to the defects are investigated by means of the numerical continuation from the anticontinuum limit and also using the variational approximation, which features a good agreement for strongly localized modes. The models with the time-modulated strengths of the linear or nonlinear defect are considered too. In that case, one can temporarily shift the critical norm, below which localized 2D modes cannot exist, to a level above the norm of the given soliton, which triggers the irreversible delocalization transition.

Dynamical stability of dipolar Bose-Einstein condensates with temporal modulation of the s-wave scattering length.

Abstract We discuss how to construct stable multidimensional extensions of one-dimensional dark solitons, the so-called soliton stripes, in two-species Bose–Einstein condensates in the immiscible regime. We show how using a second component to fill the core of a dark soliton stripe leads to reduced instabilities while propagating in homogeneous media. We also discuss how in the presence of a trap arbitrarily long-lived dark soliton stripes can be constructed by increasing the filling of the dark stripe core. Numerical evidences of the robustness of the dark soliton stripes in collision scenarios are also provided.

Scattering of Gap Solitons by PT-symmetric Defects

The propagation of solitons in dipolar BEC in a trap potential with a barrier potential is investigated. The regimes of soliton transmission, reflection and splitting as a function of the ratio between the local and dipolar nonlocal interactions are analyzed analytically and numerically. Coherent splitting and fusion of the soliton by the defect is observed. The conditions for fusion of splitted solitons are found. In addition the delocalization transition governed by the strength of the nonlocal dipolar interaction is presented. Predicted phenomena can be useful for the design of a matter wave splitter and interferometers using matter wave solitons.

Dragging two-dimensional discrete solitons by moving linear defects

We study the stabilization properties of dipolar Bose-Einstein condensate by temporal modulation of short-range two-body interaction. Through both analytical and numerical methods, we analyze the mean-field Gross-Pitaevskii equation with short-range two-body and long-range, nonlocal, dipolar interaction terms. We derive the equation of motion and effective potential of the dipolar condensate by variational method. We show that there is an enhancement of the condensate stability due to the inclusion of dipolar interaction in addition to the two-body contact interaction. We also show that the stability of the dipolar condensate increases in the presence of time varying two-body contact interaction; the temporal modification of the contact interaction prevents the collapse of dipolar Bose-Einstein condensate. Finally we confirm the semi-analytical prediction through the direct numerical simulations of the governing equation.

Localized modes in two-dimensional Schro¨dinger lattices with a pair of nonlinear sites

The resonant scattering of gap solitons of the periodic NLS equation with a PT-symmetric defect is investigated. For suitable parameters of the defect potential the resonant transmission of soliton through the defect becomes possible.

Dynamical generation of interwoven soliton trains by nonlinear emission in binary Bose-Einstein condensates

We study the mobility of small-amplitude solitons attached to moving defects which drag the solitons across a two-dimensional (2D) discrete nonlinear Schrödinger lattice. Findings are compared to the situation when a free small-amplitude 2D discrete soliton is kicked in a uniform lattice. In agreement with previously known results, after a period of transient motion the free soliton transforms into a localized mode pinned by the Peierls-Nabarro potential, irrespective of the initial velocity. However, the soliton attached to the moving defect can be dragged over an indefinitely long distance (including routes with abrupt turns and circular trajectories) virtually without losses, provided that the dragging velocity is smaller than a certain critical value. Collisions between solitons dragged by two defects in opposite directions are studied too. If the velocity is small enough, the collision leads to a spontaneous symmetry breaking, featuring fusion of two solitons into a single one, which remains attached to either of the two defects.