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We present a numerical scheme for solving the time-independent nonlinear Gross-Pitaevskii equation in two dimensions describing the Bose-Einstein condensate of trapped interacting neutral atoms at zero temperature. The trap potential is…
We study the Bose-Einstein condensation of an interacting gas with attractive interaction confined in a harmonic trap using a semiclassical two-fluid mean-field model. The condensed state is described by converged numerical solution of the…
In an atomic Bose-Einstein condensate quenched to the unitary regime, we predict the sequential formation of a significant fraction of condensed pairs and triples. At short-distances, we demonstrate the two-body and Efimovian character of…
We solve the Gross-Pitaevskii equation to model the behaviour of a weakly-interacting Bose condensate. Solutions are presented for the eigenstates in one- and two-dimensional harmonic traps. We include the effect of gravity and coupling to…
Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step…
We present previously unknown solutions to the 3D Gross--Pitaevskii equation describing atomic Bose-Einstein condensates. This model supports elaborate patterns, including excited states bearing vorticity. The discovered coherent structures…
In this paper, we study dimension reduction of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) modelling Bose-Einstein condensation under different limiting interaction and trapping frequencies parameter regimes. Convergence…
We establish the existence of strong solutions to a class of nonlinear strongly coupled and uniform elliptic systems consisting of more than two equations. The existence of of nontrivial and non constant solutions (or pattern formations)…
Based on the time-dependent Gross-Pitaevskii equation we study the evolution of a collapsing and exploding Bose-Einstein condensate in different trap symmetries to see the effect of confinement on collapse and subsequent explosion, which…
This paper deals with a class of singularly perturbed nonlinear elliptic problems $(P_\e)$ with subcritical nonlinearity. The coefficient of the linear part is assumed to concentrate in a point of the domain, as $\e\to 0$, and the domain is…
Painlev\'{e} test of the coupled Gross-Pitaevskii equations has been carried out with the result that the coupled equations pass the P-test only if a special relation containing system parameters (masses, scattering lengths) is satisfied.…
We develop a simple and general variational method to estimate the solutions of the Gross-Pitaevskii equations and obtain the corresponding density profiles for all spin states of a trapped spin-1 Bose-Einstein condensate. We further employ…
Recently, Nattermann and Pokrovsky [PRL 100, 060402 (2008)] have proposed a scaling approach for studying Bose-Einstein condensates in strongly disordered traps. In this paper we implement their scaling argument in the framework of the…
Bose-Einstein condensates of 10$^4$ $^{85}$Rb atoms in a cylindrical trap are studied using a recently proposed modified Gross-Pitaevskii equation. The existence of a Feshbach resonance allows for widely tuning the scattering length of the…
The paper considers a model for Bose gases in the so-called 'high-temperature range' below the temperature Tc, where Bose-Einstein condensation sets in.The model is of non-linear two-component type, consisting of a kinetic equation with…
Investigations on the internal one-particle density matrix in the case of Bose-Einstein condensates with a finite number ($N$) of particles in a harmonic potential are performed. We solve the eigenvalue problem of the…
The dynamics of a coupled Bose-Einstein condensate involving trapped atoms in two quantum states is studied using the time-dependent Gross-Pitaevskii equation including an interaction which can transform atoms from one state to the other.…
In this work, we study pancake-shaped Bose-Einstein condensates confined by both a cylindrically symmetric harmonic potential and an optical lattice with equal periodicity in two orthogonal directions. We first identify the spectrum of the…
We analyze the point decomposition problem (PDP) in binary elliptic curves. It is known that PDP in an elliptic curve group can be reduced to solving a particular system of multivariate non-linear system of equations derived from the so…
We study the numerical solution of the time-dependent Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate (BEC) at zero or very low temperature. In preparation for the numerics we scale the 3d Gross-Pitaevskii equation and…