26 citations · 174 across the 43 of their papers we have counts for
12 papers · 1 filter
On nonlinear Schrödinger equations with repulsive inverse-power potentials
Van Duong Dinh
In this paper, we consider the Cauchy problem for the nonlinear Schrödinger equations with repulsive inverse-power potentials \[ i \partial_t u + Δu - c |x|^{-σ} u = \pm |u|^αu, \q…
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…
Strong instability of standing waves for a system NLS with quadratic interaction
Van Duong Dinh
We study the strong instability of standing waves for a system of nonlinear Schrödinger equations with quadratic interaction under the mass resonance condition in dimension .
Existence, stability of standing waves and the characterization of finite time blow-up solutions for a system NLS with quadratic interaction
Van Duong Dinh
We study the existence and stability of standing waves for a system of nonlinear Schrödinger equations with quadratic interaction in dimensions . We also study the charact…
Blow-up criteria for fractional nonlinear Schrödinger equation
Van Duong Dinh
We consider the focusing fractional nonlinear Schrödinger equation \[ i\partial_t u - (-Δ)^s u = -|u|^αu, \quad (t,x) \in \mathbb{R}^+ \times \mathbb{R}^d, \] where …
On instability of standing waves for the mass-supercritical fractional nonlinear Schrödinger equation
Van Duong Dinh
We consider the focusing -supercritical fractional nonlinear Schrödinger equation \[ i\partial_t u - (-Δ)^s u = -|u|^αu, \quad (t,x) \in \mathbb{R}^+ \times \mathbb{R}^d, \] w…
On instability of radial standing waves for the nonlinear Schrödinger equation with inverse-square potential
Van Duong Dinh
We show the strong instability of radial ground state standing waves for the focusing -supercritical nonlinear Schrödinger equation with inverse-square potential \[ i\partial_…
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 \…
On blowup solutions to the focusing -supercritical nonlinear fractional Schrödinger equation
Van Duong Dinh
We study dynamical properties of blowup solutions to the focusing -supercritical nonlinear fractional Schrödinger equation \[ i\partial_t u -(-Δ)^s u = -|u|^αu, \quad u(0) = u…
On blowup solutions to the focusing intercritical nonlinear fourth-order Schrödinger equation
Van Duong Dinh
In this paper we study dynamical properties of blowup solutions to the focusing intercritical (mass-supercritical and energy-subcritical) nonlinear fourth-order Schrödinger equatio…
On Blowup solutions to the focusing mass-critical nonlinear fractional Schrödinger equation
Van Duong Dinh
In this paper we study dynamical properties of blowup solutions to the focusing mass-critical nonlinear fractional Schrödinger equation. We establish a profile decomposition and a…