Related papers: Integrability of two-component nonautonomous nonli…

We find one-, two-, and three-component solitons of the polar and ferromagnetic (FM) types in the general (non-integrable) model of a spinor (three-component) model of the Bose-Einstein condensate (BEC), based on a system of three…

We derive the dynamic and thermodynamic stability conditions for dilute multicomponent Bose-Einstein condensates (BECs). These stability conditions, generalized for $n$-component BECs, are found to be equivalent and are shown to be…

We study the effect of a logarithmic nonlinearity in the Schr\"odinger equation (SE) on the dynamics of a freely expanding Bose-Einstein condensate (BEC). The logarithmic nonlinearity was one of the first proposed nonlinear extensions to…

We report results of systematic simulations of the dynamics of solitons in the framework of the one-dimensional nonlinear Schr\"{o}dinger equation (NLSE), which includes the harmonic-oscillator (HO) potential and a random potential. The…

Coupled nonlinear Schrodinger equations (CNLS) with an external elliptic function potential model a quasi one--dimensional interacting two-component Bose-Einstein condensate trapped in a standing light wave. New families of stationary…

We study modulational instability of two-component Bose-Einstein condensates in an optical lattice, which is modelled as a coupled discrete nonlinear Schr \"{o}dinger equation. The excitation spectrum and the modulational instability…

Dynamics of vector dark solitons in two-component Bose-Einstein condensates is studied within the framework of the coupled one-dimensional nonlinear Schr\"odinger (NLS) equations. We consider the small amplitude limit in which the coupled…

The designable integrability(DI) of the variable coefficient nonlinear Schr\"odinger equation (VCNLSE) is first introduced by construction of an explicit transformation which maps VCNLSE to the usual nonlinear Schr\"odinger equation(NLSE).…

We study the dynamical phase diagram of a dilute Bose-Einstein condensate (BEC) trapped in a periodic potential. The dynamics is governed by a discrete non-linear Schr\"odinger equation: intrinsically localized excitations, including…

It is shown that the one-dimensional nonlinear Schr\"odinger equation with a dissipative periodic potential, nonlinear losses and linear pump allow for the existence of stable nonlinear Bloch states which are attractors. The model describes…

The strongly interacting regime for attractive Bose-Einstein condensates (BECs) tightly confined in an extended cylindrical trap is studied. For appropriately prepared, non-collapsing BECs, the ensuing dynamics are found to be governed by…

We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schr\"odinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic field, and confined in a strong optical…

We study fundamental and vortical solitons in disk-morphed Bose-Einstein condensates (BECs) subject to strong confinement along the axial direction. Starting from the three-dimensional (3D) Gross-Pitaevskii equation (GPE), we proceed to an…

We consider the three-dimensional (3D) mean-field model for the Bose-Einstein condensate (BEC), with a 1D nonlinear lattice (NL), which periodically changes the sign of the nonlinearity along the axial direction, and the harmonic-oscillator…

We present a series of experimental investigations on binary mixtures of Bose-Einstein condensates. Our focus lies on the regime where the interaction parameters place the system at the threshold of miscibility. We demonstrate that the…

A three- and five-component nonlinear Schrodinger-type models, which describe spinor Bose-Einstein condensates (BEC's) with hyperfine structures F=1 and F=2 respectively, are studied. These models for particular values of the coupling…

Nonlinearity in the Schr\"odinger equation gives rise to rich phenomena such as soliton formation, modulational instability, and self-organization in diverse physical systems. Motivated by recent advances in engineering nonlinear gauge…

In this paper, we study the following two-component systems of nonlinear Schr\"odinger equations \begin{equation*} \left\{\aligned&\Delta u-(\lambda a(x)+a_0(x))u+\mu_1u^3+\beta v^2u=0\quad&\text{in }\bbr^3,\\ &\Delta v-(\lambda…

We introduce a model motivated by studies of Bose-Einstein condensates (BECs) trapped in double-well potentials. We assume that a mixture of two hyperfine states of the same atomic species is loaded in such a trap.The analysis is focused on…

We model the nonlinear behaviour of spin-1 Bose-Einstein condensates (BECs) with repulsive spin-independent interactions and either ferromagnetic or anti-ferromagnetic (polar) spin-dependent interactions, loaded into a one-dimensional…