26 citations · 174 across the 43 of their papers we have counts for
9 papers · 2 filters
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…
Blow-up results for systems of nonlinear Schrödinger equations with quadratic interaction
Van Duong Dinh, Luigi Forcella
We establish blow-up results for systems of NLS equations with quadratic interaction in anisotropic spaces. We precisely show finite time blow-up or grow-up for cylindrical symmetr…
On stability of rotational 2D binary Bose-Einstein condensates
Rémi Carles, Van Duong Dinh, Hichem Hajaiej
We consider a two-dimensional nonlinear Schr{ö}dinger equation proposed in Physics to model rotational binary Bose-Einstein condensates. The nonlinearity is a logarithmic modificat…
Random data theory for the cubic fourth-order nonlinear Schrödinger equation
Van Duong Dinh
We consider the cubic nonlinear fourth-order Schrödinger equation \[ i\partial_t u - Δ^2 u + μΔu = \pm |u|^2 u, \quad μ\geq 0 \] on with random initial dat…
Mass-Energy threshold dynamics for dipolar Quantum Gases
Van Duong Dinh, Luigi Forcella, Hichem Hajaiej
We consider a Gross-Pitaevskii equation which appears as a model in the description of dipolar Bose-Einstein condensates, without a confining external trapping potential. We descri…
Long time dynamics for the focusing nonlinear Schrödinger equation with exponential nonlinearities
Van Duong Dinh, Sahbi Keraani, Mohamed Majdoub
In this paper, we study the focusing nonlinear Schrödinger equation with exponential nonlinearities \[ i \partial_t u + Δu = - \left(e^{4π|u|^2} - 1 - 4πμ|u|^2 \right) u, \quad u(0…
Blow-up criteria for linearly damped nonlinear Schrödinger equations
Van Duong Dinh
We consider the Cauchy problem for linearly damped nonlinear Schrödinger equations \[ i\partial_t u + Δu + i a u= \pm |u|^αu, \quad (t,x) \in [0,\infty) \times \mathbb{R}^N, \] whe…
Dynamics of radial solutions for the focusing fourth-order nonlinear Schrödinger equations
Van Duong Dinh
We consider the following class of focusing -supercritical fourth-order nonlinear Schrödinger equations \[ i\partial_t u - Δ^2 u + μΔu = - |u|^αu, \quad (t,x) \in \mathbb{R} \…
Non-radial scattering theory for nonlinear Schrödinger equations with potential
Van Duong Dinh
We consider a class of nonlinear Schrödinger equations with potential \[ i\partial_t u +Δu - Vu = \pm |u|^αu, \quad (t,x) \in \mathbb{R} \times \mathbb{R}^3, \] where $\frac{4}{3}<…