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We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates of weakly interacting alkali atoms described by a nonlinear Gross-Pitaevskii (GP) equation. We suggest a pseudospectral method involving Laguerre…
We study the formation of singularities for cylindrical symmetric solutions to the Gross-Pitaevskii equation describing a dipolar Bose-Einstein condensate. We prove that solutions arising from initial data with energy below the energy of…
We study a mechanism of collapse of the condensate wave function in the Gross-Pitaevskii theory with attractive interparticle interaction. We reformulate the Gross-Pitaevskii equation as Newton's equations for the particle flux and…
The dynamics of stability and collapse of a trapped atomic Bose-Einstein condensate (BEC) coupled to a molecular one is studied using the time-dependent Gross-Pitaevskii (GP) equation including a nonlinear interaction term which can…
We study the mechanisms of the gravitational collapse of the Bose-Einstein condensate dark matter halos, described by the zero temperature time-dependent nonlinear Schr\"odinger equation (the Gross-Pitaevskii equation), with repulsive…
We consider the Gross-Pitaevskii (GP) equation in the presence of periodic and quasiperiodic superlattices to study cigar-shaped Bose-Einstein condensates (BECs) in such potentials. We examine spatially extended wavefunctions in the form of…
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…
Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate under periodic variation in time of the atomic scattering length have been studied analytically and numerically. The time-dependent variational approach is used for…
We experimentally investigate the collapse dynamics of dipolar Bose- Einstein condensates of chromium atoms in different harmonic trap geometries, from prolate to oblate. The evolutions of the condensates in the unstable regime are compared…
We analyse a generalised Gross-Pitaevskii equation involving a paraboloidal trap potential in $D$ space dimensions and generalised to a nonlinearity of order $2n+1$. For {\em attractive} coupling constants collapse of the particle density…
We explore the effect of mutual gravitational interaction between ultra-cold gas atoms on the dynamics of Bose-Einstein condensates (BEC). Small amplitude oscillation of BEC is studied by applying variational technique to reduce the…
Long-lived, spatially localized, and temporally oscillating nonlinear excitations are predicted by numerical simulation of coupled Gross-Pitaevskii equations. These oscillons closely resemble the time-periodic breather solutions of the…
The discovery of a "weakly-turbulent" instability of anti-de Sitter spacetime supports the idea that confined fluctuations eventually collapse to black holes and suggests that similar phenomena might be possible in asymptotically-flat…
We numerically simulate gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative…
In flat spacetime, quantum fluctuations in dark matter, as described as a Bose-Einstein condensate, are stable and display a relativistic Bogoliubov dispersion relation. In the weak gravitational field limit, both relativistic and…
We analyse systematically, from the viewpoint of the nonlinear physics of solitary waves, the effect of the spatial dimension (D = 1,2,3) on the structure and stability of the Bose-Einstein condensates (BECs) trapped in an external…
We present an action that can be used to study variationally the collapse of Bose Einstein condensates. This action is real, even though it includes dissipative terms. It adopts long range interactions between the atoms, so that there is…
We investigate the dynamics of a Bose-Einstein condensate in a progressively bended three dimensional cigar shaped potential. The interplay between geometry and nonlinearity is considered. At high curvature, topological localization occurs…
We study the structure, stability, and dynamics of dark solitary waves in parabolically trapped, collisionally inhomogeneous Bose-Einstein condensates (BECs) with spatially periodic variations of the scattering length. This collisional…
Four-dimensional cylindrically symmetric spacetimes with homothetic self-similarity are studied in the context of Einstein's Theory of Gravity, and a class of exact solutions to the Einstein-massless scalar field equations is found. Their…