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We consider a system of Gross-Pitaevskii equations in R^2 modelling a mixture of two Bose-Einstein condensates with repulsive interaction. We aim to study the qualitative behaviour of ground and excited state solutions. We allow two different harmonic and off-centered trapping potentials and study the spatial patterns of the solutions within the Thomas-Fermi approximation as well as phase segregation phenomena within the large-interaction regime.
We prove existence and qualitative properties of ground state solutions to a generalized nonlocal 3rd-4th order Gross-Pitaevskii equation. Using a mountain pass argument on spheres and constructing appropriately localized Palais-Smale sequences we ar
We study the Cauchy problem for the 3D Gross-Pitaevskii equation. The global well-posedness in the natural energy space was proved by Gerard cite{Gerard}. In this paper we prove scattering for small data in the same space with some additional angular
The purpose of this paper is to provide a rigorous mathematical proof of the existence of travelling wave solutions to the Gross-Pitaevskii equation in dimensions two and three. Our arguments, based on minimization under constraints, yield a full bra
We consider the 3D Gross-Pitaevskii equation begin{equation} onumber ipartial_t psi +Delta psi+(1-|psi|^2)psi=0 text{ for } psi:mathbb{R}times mathbb{R}^3 rightarrow mathbb{C} end{equation} and construct traveling waves solutions to this equation. Th
We investigate the existence of ground state solutions of a Gross-Pitaevskii equation modeling the dynamics of pumped Bose Einstein condensates (BEC). The main interest in such BEC comes from its important nature as macroscopic quantum system, consti