45 citations · 148 across the 22 of their papers we have counts for
26 papers
Soliton Dynamics for the Cubic-Quintic Nonlinear Schrödinger Equation with a Potential
Alex H. Ardila, Rémi Carles
We study the semiclassical dynamics of solitary waves for the three-dimensional cubic--quintic nonlinear Schrödinger equation with an external potential. For initial data given by…
Blow-up or grow-up for the focusing 3D cubic NLS with a repulsive inverse-power potential at the mass--energy threshold
Alex H. Ardila, Zuyu Ma, Ying Wang
We consider the focusing cubic nonlinear Schrodinger equation with a repulsive inverse-power potential , where and . At the mass-energy threshold,…
Threshold dynamics for the 4 mass-energy double critical NLS
Alex H. Ardila, Zuyu Ma, Jason Murphy +1
We consider the 4 mass-energy double critical NLS \[ (i\partial_t+Δ)u = -|u|^2 u + |u| u. \] In Luo (2024) and Cheng--Miao--Zhao (2016), the authors established a scattering/blo…
Dynamics of the Energy-Critical Nonlinear Schrödinger System in
Alex H. Ardila
In this paper, we investigate the dynamics of radial solutions at threshold energy for a 3-component Schrödinger system with cubic nonlinearity in four dimensions. The main differe…
Threshold solutions for the energy-critical NLS system with quadratic interaction
Alex H. Ardila, Liliana Cely, Fanfei Meng
In this paper, we study the Cauchy problem for a quadratic nonlinear Schrödinger system in dimension six. In~\cite{GaoMengXuZheng}, the authors classified the behavior of solutions…
Threshold dynamics for the 3 radial NLS with combined nonlinearity
Alex H. Ardila, Jason Murphy, Jiqiang Zheng
We consider the nonlinear Schrödinger equation with focusing quintic and defocusing cubic nonlinearity in three space dimensions: \[ (i\partial_t+Δ)u = |u|^2 u - |u|^4 u. \] In [18…
Threshold solutions for the 3d cubic-quintic NLS
Alex H. Ardila, Jason Murphy
We study the cubic-quintic NLS in three space dimensions. It is known that scattering holds for solutions with mass-energy in a region corresponding to positive virial, the boundar…
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…
The cubic-quintic nonlinear Schrödinger equation with inverse-square potential
Alex H. Ardila, Jason Murphy
We consider the nonlinear Schrödinger equation in three space dimensions with a focusing cubic nonlinearity and defocusing quintic nonlinearity and in the presence of an external i…
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…
Global well-posedness, blow-up and stability of standing waves for supercritical NLS with rotation
Alex H. Ardila, Hichem Hajaiej
We consider the focusing mass supercritical nonlinear Schrödinger equation with rotation \begin{equation*} iu_{t}=-\frac{1}{2}Δu+\frac{1}{2}V(x)u-|u|^{p-1}u+L_Ωu,\quad (x,t)\in \ma…
Global dynamics below the ground states for NLS under partial harmonic confinement
Alex Ardila, Rémi Carles
We are concerned with the global behavior of the solutions of the focusing mass supercritical nonlinear Schr{ö}dinger equation under partial harmonic confinement. We establish a ne…
Some qualitative studies of the focusing inhomogeneous Gross-Pitaevskii equation
Alex H. Ardila, Van Duong Dinh
We study the Cauchy problem for an inhomogeneous Gross-Pitaevskii equation. We first derive a sharp threshold for global existence and blow up of the solution. Then we construct an…
Orbital stability of standing waves for supercritical NLS with potential on graphs
Alex H. Ardila
In this paper we study the existence and stability of normalized standing waves for the nonlinear Schrödinger equation on a general starlike graph with potentials. Under general as…
Logarithmic Bose-Einstein condensates with harmonic potential
Alex H. Ardila, Liliana Cely, Marco Squassina
In this paper, by using a compactness method, we study the Cauchy problem of the logarithmic Schrödinger equation with harmonic potential. We then address the existence of ground s…
Orbital stability of standing waves for a system of nonlinear Schrödinger equations with three wave interaction
Alex H. Ardila
We study the existence and stability of standing waves solutions of a three-coupled nonlinear Schrödinger system related to the Raman amplification in a plasma. By means of the con…
Gausson dynamics for logarithmic Schrödinger equations
Alex H. Ardila, Marco Squassina
In this paper we study the validity of a Gausson (soliton) dynamics of the logarithmic Schrödinger equation in presence of a smooth external potential.
Existence and stability of standing waves for nonlinear fractional Schrödinger equation with logarithmic nonlinearity
Alex Hernandez Ardila
In this paper we consider the nonlinear fractional logarithmic Schrödinger equation. By using a compactness method, we construct a unique global solution of the associated Cauchy p…
Logarithmic NLS equation on star graphs: existence and stability of standing waves
Alex H. Ardila
In this paper we consider the logarithmic Schrödinger equation on a star graph. By using a compactness method, we construct a unique global solution of the associated Cauchy proble…
Stability of ground states for logarithmic Schrödinger equation with a -interaction
Alex Hernandez Ardila
In this paper we study the one-dimensional logarithmic Schrödinger equation perturbed by an attractive -interaction \[ i\partial_{t}u+\partial^{2}_{x}u+ γδ^{\prime}(x)u…