25 citations · 25 across the 6 of their papers we have counts for
11 papers
Mass-energy threshold dynamics for the focusing NLS with a repulsive inverse-power potential
Alex H. Ardila, Masaru Hamano, Masahiro Ikeda
In this paper we study long time dynamics (i.e., scattering and blow-up) of solutions for the focusing NLS with a repulsive inverse-power potential and with initial data lying exac…
Threshold scattering for the focusing NLS with a repulsive Dirac delta potential
Alex H. Ardila, Takahisa Inui
We establish the scattering of solutions to the focusing mass supercritical nonlinear Schrödinger equation with a repulsive Dirac delta potential \[ i\partial_{t}u+\partial^{2}_{x}…
Blow-up and scattering for the 1D NLS with point nonlinearity above the mass-energy threshold
Alex H. Ardila
In this paper, we study the nonlinear Schrödinger equation with focusing point nonlinearity in dimension one. First, we establish a scattering criterion for the equation based on K…
Instability of ground states for the NLS equation with potential on the star graph
Alex H. Ardila, Liliana Cely, Nataliia Goloshchapova
We study the nonlinear Schrödinger equation with an arbitrary real potential on a star graph . At the vertex an interaction occurs described by the g…
Sharp conditions for scattering and blow-up for a system of NLS arising in optical materials with nonlinear response
Alex H. Ardila, Van Duong Dinh, Luigi Forcella
We study the asymptotic dynamics for solutions to a system of nonlinear Schrödinger equations with cubic interactions, arising in nonlinear optics. We provide sharp threshold crite…
Scattering of the energy-critical NLS with dipolar interaction
Alex H. Ardila
In this paper, we investigate the global well-posedness and scattering theory for a 3d energy-critical Schrödinger equation under the influence of magnetic dipole interacti…