Related papers: On stability of rotational 2D binary Bose-Einstein…
The paradigm of Bose-Einstein condensation has been associated with zero momentum to which a macroscopic fraction of bosons condense. Here we propose a new quantum state where bosonic alkali-metal atoms condense at non-zero momenta, defying…
We introduce a two-dimensional (2D) discrete nonlinear Schr\"{o}dinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong…
We revisit the problem of the reduction of the three-dimensional (3D) dynamics of Bose-Einstein condensates, under the action of strong confinement in one direction ($z$), to a 2D mean-field equation. We address this problem for the…
We study dynamical properties of the cubic lowest Landau level equation, which is used in the modeling of fast rotating Bose-Einstein condensates. We obtain bounds on the decay of general stationary solutions. We then provide a…
The modulational instability of spatially uniform states in the nonlinear Schr\"odinger equation is examined in the presence of higher-order dissipation. The study is motivated by results on the effects of three-body recombination in…
We present variational and numerical solutions for the problem of stability of persistent currents in a two-component Bose-Einstein condensate of distinguishable atoms which rotate in a ring potential. We consider the general class of…
We demonstrate the existence of localized oscillatory breathers for quasi-one-dimensional Bose-Einstein condensates confined in periodic potentials. The breathing behavior corresponds to position-oscillations of individual condensates about…
On a star graph made of $N \geq 3$ halflines (edges) we consider a Schr\"odinger equation with a subcritical power-type nonlinearity and an attractive delta interaction located at the vertex. From previous works it is known that there…
The possibility of effectively inverting the sign of the dipole-dipole interaction, by fast rotation of the dipole polarization, is examined within a harmonically trapped dipolar Bose-Einstein condensate. Our analysis is based on the…
It was recently found that the spin-orbit (SO) coupling can help to create stable matter-wave solitons in spinor Bose-Einstein condensates in the two-dimensional (2D) free space. Being induced by external laser illumination, the effective…
We consider a trapped dilute gas of $N$ bosons in $\mathbb{R}^3$ interacting via a three-body interaction potential of the form $N\, V(N^{1/2}(x-y,x-z))$. In the limit $N\to \infty$, we prove that every approximate ground state of the…
We perform a detailed numerical study of the equilibrium ground-state structures of a binary rotating Bose-Einstein condensate with unequal atomic masses. Our results show that the ground-state distribution and its related vortex…
We study the stability of a Bose-Einstein condensate of harmonically trapped atoms with negative scattering length, specifically lithium 7. Our method is to solve the time-dependent nonlinear Schrodinger equation numerically. For an…
In this paper, we study normalized solutions to the Chern-Simons-Schr\"odinger system, which is a gauge-covariant nonlinear Sch\"oridnger system with a long-range electromagnetic field, arising in nonrelativistic quantum mechanics theory.…
We study the Bloch dynamics of a quasi one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type: The corresponding mean-field system described by a discrete nonlinear…
We present effective reduced equations for the study of a binary Bose-Einstein condensate (BEC), where the confining potentials of the two BEC components have distinct asymmetry so that the components belong to different space dimensions as…
In this work, we would like to present the Bose-Einstein Condensation in such a system where rotation is decreasing radially from the centre of the condensate. That non-uniform rotation is defined by a rotating parameter called $\lambda$.…
We study the stationary nonlinear Schr\"odinger equation, or Gross-Pitaevskii equation, for a one--dimensional finite square well potential. By neglecting the mean--field interaction outside the potential well it is possible to discuss the…
We study the existence and stability of standing waves solutions of a three-coupled nonlinear Schr\"{o}dinger system related to the Raman amplification in a plasma. By means of the concentration-compacteness method, we provide a…
We study the following doubly critical Schr\"{o}dinger system $$-\Delta u -\frac{\la_1}{|x|^2}u=u^{2^\ast-1}+ \nu \al u^{\al-1}v^\bb, \quad x\in \RN, -\Delta v -\frac{\la_2}{|x|^2}v=v^{2^\ast-1} + \nu \bb u^{\al}v^{\bb-1}, \quad x\in \RN,…