Christos Sourdis

Thomas–Fermi Approximation for Coexisting Two Component Bose–Einstein Condensates and Nonexistence of Vortices for Small Rotation

We study minimizers of a Gross–Pitaevskii energy describing a two- component Bose–Einstein condensate confined in a radially symmetric harmonic trap and set into rotation. We consider the case of coexistence of the components in the Thomas–Fermi regime, where a small parameter

Analysis of the heteroclinic connection in a singularly perturbed system arising from the study of crystalline grain boundaries

{\varepsilon}

On the existence of dark solitons of the defocusing cubic nonlinear Schrödinger equation with periodic inhomogeneous nonlinearity

ε conveys a singular perturbation. The minimizer of the energy without rotation is determined as the positive solution of a system of coupled PDEs, for which we show uniqueness. The limiting problem for

Heteroclinic Orbits in Slow-Fast Hamiltonian Systems with Slow Manifold Bifurcations

{\varepsilon =0}

The Heteroclinic Connection Problem for General Double-Well Potentials

ε=0 has degenerate and irregular behavior at specific radii, where the gradient blows up. By means of a perturbation argument, we obtain precise estimates for the convergence of the minimizer to this limiting profile, as