Related papers: Matter-wave solitons in radially periodic potentia…
The existence of stable solitons in two- and three-dimensional (2D and 3D) media governed by the self-focusing cubic nonlinear Schr\"{o}dinger equation with a periodic potential is demonstrated by means of the variational approximation (VA)…
We study the dynamics of one-dimensional solitons in the attractive and repulsive Bose-Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. First, we demonstrate…
We study the statics and dynamics of anisotropic, stable, bright and dark-in-bright dipolar quasi-two-dimensional Bose-Einstein condensate (BEC) solitons on a one-dimensional (1D) optical-lattice (OL) potential. These solitons mobile in a…
We present a theoretical analysis of three-dimensional (3D) matter-wave solitons and their stability properties in coupled atomic and molecular Bose-Einstein condensates (BEC). The soliton solutions to the mean-field equations are obtained…
We examine the dynamics of a bright solitary wave in the presence of a repulsive or attractive localized ``impurity'' in Bose-Einstein condensates (BECs). We study the generation and stability of a pair of steady states in the vicinity of…
We demonstrate a possibility to generate localized states in effectively one-dimensional Bose-Einstein condensates with a negative scattering length in the form of a dark soliton in the presence of an optical lattice (OL) and/or a parabolic…
We review the state of the art and recently obtained theoretical and experimental results for two- and three-dimensional (2D and 3D) solitons and related states, such as quantum droplets, in optical systems, atomic Bose-Einstein condensates…
We discuss localized ground states of Bose-Einstein condensates in optical lattices with attractive and repulsive three-body interactions in the framework of a quintic nonlinear Schr\"odinger equation which extends the Gross-Pitaevskii…
We develop a systematic analytical approach to study the linear and nonlinear solitary excitations of quasi-one-dimensional Bose-Einstein condensates trapped in an optical lattice. For the linear case, the Bloch wave in the $nth$ energy…
We consider two-dimensional spin-orbit coupled atomic Bose-Einstein condensate in a radially-periodic potential. The system supports different types of stable self-sustained states including radially-symmetric vorticity-carrying modes with…
We report on the existence and stability of multidimensional bound solitonic states in harmonically-trapped scalar Bose-Einstein condensates. Their equilibrium separation, as a measure of the strength of the soliton-soliton or the solitonic…
We investigate magnetic solitons in an immiscible binary Bose-Einstein condensate (BEC), where the intraspecies interactions are slightly weaker than the interspecies interactions. While their density and phase profiles are analogous to…
We investigate the ground state (GS) of a collisionless Bose-Einstein condensate (BEC) trapped in a soft one-dimensional optical lattice (OL), which is formed by two counterpropagating optical beams perturbed by the BEC density profile…
Models of two-dimensional (2D) traps, with the double-well structure in the third direction, for Bose-Einstein condensate (BEC) are introduced, with attractive or repulsive interactions between atoms. The models are based on systems of…
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…
We demonstrate robust, stable, mobile excited states of quasi-two-dimensional (quasi-2D) dipolar Bose-Einstein condensate (BEC) solitons for repulsive contact interaction with a harmonic trap along the $x$ direction perpendicular to the…
We study two-dimensional (2D) matter-wave solitons in spinor Bose-Einstein condensates (BECs) under the action of the spin-orbit coupling (SOC) and opposite signs of the self- and cross-interactions. Stable 2D two-component solitons of the…
We analyze the existence and stability of two kinds of self-trapped spatially localized gap modes, gap solitons and truncated nonlinear Bloch waves, in one-and two-dimensional optical or matter-wave media with self-focusing nonlinearity,…
We study matter-wave bright solitons in spin-orbit (SO) coupled Bose-Einstein condensates (BECs) with attractive interatomic interactions. We use a multiscale expansion method to identify solution families for chemical potentials in the…
Density-wave patterns in (quasi-) discrete media with local interactions are known to be unstable. We demonstrate that \emph{stable} double- and triple- period patterns (DPPs and TPPs), with respect to the period of the underlying lattice,…