6 papers
A 2D Schrodinger equation with time-oscillating exponential nonlinearity
Abdelwahab Bensouilah, Dhouha Draouil, Mohamed Majdoub
This paper deals with the 2-D Schrödinger equation with time-oscillating exponential nonlinearity , where is a periodic -fu…
Scattering in the weighted -space for a 2D nonlinear Schrödinger equation with inhomogeneous exponential nonlinearity
Abdelwahab Bensouilah, Van Duong Dinh, Mohamed Majdoub
We investigate the defocusing inhomogeneous nonlinear Schrödinger equation $$ i \partial_tu + Δu = |x|^{-b} \left({\rm e}^{α|u|^2} - 1- α|u|^2 \right) u, \quad u(0)=u_0, \quad x \i…
On stability and instability of standing waves for the nonlinear Schrödinger equation with inverse-square potential
Abdelwahab Bensouilah, Van Duong Dinh, Shihui Zhu
We consider the focusing nonlinear Schrödinger equation with inverse square potential \[ i\partial_t u + Δu + c|x|^{-2} u = - |u|^αu, \quad u(0) = u_0 \in H^1, \quad (t,x) \in \mat…
Mass concentration and characterization of finite time blow-up solutions for the nonlinear Schrödinger equation with inverse-square potential
Abdelwahab Bensouilah, Van Duong Dinh
We consider the -critical NLS with inverse-square potential $$ i \partial_t u +Δu + c|x|^{-2} u = -|u|^{\frac{4}{d}} u, \quad u(0) = u_0, \quad (t,x) \in \mathbb{R}^+ \times \…
concentration of blow-up solutions for the mass-critical NLS with inverse-square potential
Abdelwahab Bensouilah
In this paper, we prove a refined version of a compactness lemma and we use it to establish mass-concentration for the focusing nonlinear Schrödinger equation with an inverse-squar…
Energy critical Schrödinger equation with weighted exponential nonlinearity I: Local and global well-posedness
Abdelwahab Bensouilah, Dhouha Draouil, Mohamed Majdoub
We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with weighted exponential nonlinearity $$ i\partial_t u+Δu=\frac{u}{|x|^b}(e^{α|u|^2}-1); \…