Related papers: Gross-Pitaevskii non-linear dynamics for pseudo-sp…
We analyze a system of coupled Bose-Einstein condensates in the domain of a unitary ball in $\mathbb{R}^3$. The coupling is due to atom-to-atom interactions that occur between different gas components. The multi-component Bose-Einstein…
We present a study of binary mixtures of Bose-Einstein condensates confined in a double-well potential within the framework of the mean field Gross-Pitaevskii equation. We reexamine both the single component and the binary mixture cases for…
We investigate the properties of discrete breathers in a Bose-Einstein condensate with two- and three-body interactions in optical lattice. In the tight-binding approximation the Gross-Pitaevskii equation with periodic potential for the…
We describe recent development of quantum hydrodynamics for ultracold Bose particle studying and consider different kinds of interactions. The method of derivation of equations describing the evolution of the neutral Bose particle system at…
We numerically simulate the creation process of two-dimensional skyrmionic excitations in antiferromagnetic spin-1 Bose--Einstein condensates by solving the full three-dimensional dynamics of the system from the Gross--Pitaevskii equation.…
We study the nonlinear localized modes in two-component Bose-Einstein condensates with parity-time-symmetric Scarf-II potential, which can be described by the coupled Gross-Pitaevskii equations. Firstly, we investigate the linear stability…
A phenomenological model is proposed to describe the behavior of spinor Bose-Einstein condensates. In the absence of hyperfine spin-spin interactions, Bose-Einstein condensation leads to a spontaneous magnetization at the same transition…
The stochastic Gross-Pitaevskii equation represents a versatile approach for studying the dynamics of trapped degenerate ultracold Bose gases in the presence of large phase and density fluctuations. Following a brief review of the original…
We report on some recent results regarding the dynamical behavior of a trapped Bose-Einstein condensate, in the limit of a large number of particles. These results were obtained in \cite{ESY}, a joint work with L. Erd\H os and H.-T. Yau.
We investigate the dynamics of bright matter wave solitons in spin-1 Bose-Einstein condensates with time modulated nonlinearities. We obtain soliton solutions of an integrable autonomous three-coupled Gross-Pitaevskii (3-GP) equations using…
We consider a many-body system of pseudo-spin-1/2 bosons with spin-orbit interactions, which couple the momentum and the internal pseudo-spin degree of freedom created by spatially varying laser fields. The corresponding single- particle…
We study the Gross-Pitaevskii (GP) energy functional for a fast rotating Bose-Einstein condensate on the unit disc in two dimensions. Writing the coupling parameter as $ 1 / \eps^2 $ we consider the asymptotic regime $ \eps \to 0 $ with the…
In a spinor Bose-Einstein gas, the non-zero hyperfine spin of the gas becomes an accessible degree of freedom. At low temperature, such a gas shows both magnetic and superfluid order, and undergoes both density and spin dynamics. These…
In this paper we present analytical breather solutions of the three-dimensional nonlinear generalized Gross-Pitaevskii equation. We use an Ansatz to reduce the three-dimensional equation with space- and time-dependent coefficients into an…
The ground state of a gas of Bosons confined in an external trap potential and interacting via repulsive two-body forces has recently been shown to exhibit complete Bose-Einstein condensation in the dilute limit, yielding for the first time…
In the hydrodynamic approximation we obtain analytic solutions to the Gross-Pitaevskii equation with positive scattering length which describe expansions of the Bose-Einstein condensates in quasi-one and quasi-two dimensional geometries.…
We introduce a dissipation term in the Gross-Pitaevskii equation that describes the stimulated relaxation of condensed bosons due to scattering with a different type of particles. This situation applies to Bose-Einstein condensates of…
We consider the dynamics of dark matter solitons moving through non-uniform cigar-shaped Bose-Einstein condensates described by the mean field Gross-Pitaevskii equation with generalized nonlinearities, in the case when the condition for the…
We present a method for evolving the projected Gross-Pitaevskii equation in an infinite rotating Bose-Einstein condensate, the ground state of which is a vortex lattice. We use quasi-periodic boundary conditions to investigate the behaviour…
In this paper, we have studied the integrability nature of a system of three coupled Gross-Pitaevskii type nonlinear evolution equations arising in the context of spinor Bose-Einstein condensates by applying the Painlev\'e singularity…