Solitons in tunnel-coupled repulsive and attractive condensates

We study solitons in the condensate trapped in a double-well potential with far-separated wells, when the s-wave scattering length has different signs in the two parts of the condensate. By employing the coupled-mode approximation it is shown that there are unusual stable bright solitons in the condensate, with the larger share of atoms being gathered in the repulsive part. Such unusual solitons derive their stability from the quantum tunneling and correspond to the strong coupling between the parts of the condensate. The ground state of the system, however, corresponds to weak coupling between the condensate parts, with the larger share of atoms being gathered in the attractive part of the condensate.Comment: LaTex, 23 pages, 6 figures; revised version; to appear in Physical Review

Mixed-isotope Bose-Einstein condensates in Rubidium

We consider the ground state properties of mixed Bose-Einstein condensates of 87Rb and 85Rb atoms in the isotropic pancake trap, for both signs of the interspecies scattering length. In the case of repulsive interspecies interaction, there are the axially-symmetric and symmetry-breaking ground states. The threshold for the symmetry breaking transition, which is related to appearance of a zero dipole-mode, is found numerically. For attractive interspecies interactions, the two condensates assume symmetric ground states for the numbers of atoms up to the collapse instability of the mixture.Comment: Revised; 21 pages, 5 figures, submitted to Physical Review

Resonances in a trapped 3D Bose-Einstein condensate under periodically varying atomic scattering length

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 the analysis of the characteristics of nonlinear resonances in the oscillations of the condensate. The bistability in oscillations of the BEC width is invistigated. The dependence of the BEC collapse threshold on the drive amplitude and parameters of the condensate and trap is found. Predictions of the theory are confirmed by numerical simulations of the full Gross-Pitaevski equation.Comment: 17 pages, 10 figures, submitted to Journal of Physics

Modelling the COVID-19 pandemic in context : An international participatory approach

Funding RA is funded by the Bill and Melinda Gates Foundation (OPP1193472). LW is funded by the Li Ka Shing Foundation. CF is funded by grant #2017/26770-8, São Paulo Research Foundation (FAPESP). The CoMo Consortium has support from the Oxford University COVID-19 Research Response Fund (ref: 0009280). Scientific writing assistance and editorial support was provided by Adam Bodley, according to Good Publication Practice guidelines.Peer reviewedPublisher PD

Two-dimensional integrable generalization of the Camassa-Holm equation

In this letter we discuss the (2 + 1)-dimensional generalization of the Camassa-Holm equation. We require that this generalization be, at the same time, integrable and physically derivable under the same asymptotic analysis as the original Camassa-Holm equation. First, we find the equation in a perturbative calculation in shallow-water theory. We then demonstrate its integrability and find several particular solutions describing (2 + 1) solitary-wave like solutions. © 1999 Published by Elsevier Science B.V. All rights reserved

Vortices in nonlocal Gross-Pitaevskii equation

Abstract. We consider vortices in nonlocal Gross-Pitaevskii model in two dimensions with the interaction potential having the Lorentz-shaped dependence on the relative momentum. First, we analytically prove that, in the Fourier series expansion with respect to the polar angle, the unstable modes of the axial n-fold vortex have orbital numbers l satisfying 0 < |l | < 2|n|, similar as in the local model. Second, we numerically study the stability properties of the axial n-vortex solutions in the nonlocal model. It is found that nonlocality has little effect on the critical nucleation frequency of the 1-vortex, but decreases the frequency of its anomalous mode. In the case of higher axial vortices there are instability against splitting intervals of the interaction range and (possibly) additional anomalous modes with higher orbital numbers. On the other hand, the structure of the energy minimizing vortex solutions proves to be insensitive to the range of interaction: the same solutions are energy minimizers for nonlocal and local models. Our results can have applications for the phenomenological description of topological defects in superfluid helium and superconductors. PACS numbers: 03.75.Lm, 03.75.NtVortices in nonlocal Gross-Pitaevskii equation 2 1

Modified Korteweg-de Vries hierarchy with hodograph transformation: Camassa-Holm and Harry-Dym hierarchies

In this paper, we present relations between Camassa-Holm (CH), Harry-Dym (HD) and modified Korteweg-de Vries (mKdV) hierarchies, which are given by the hodograph type transformation. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved