66 citations · 187 across the 25 of their papers we have counts for
16 papers · 1 filter
local exact controllability of some one-dimensional bilinear Schr{ö}dinger equations
Nabile Boussaïd, Alessandro Duca
The local exact controllability of the one-dimensional bilinear Schr{ö}dinger equation with Dirichlet boundary conditions has been extensively studied in subspaces of H 3 since the…
Existence of stationary solutions of supercritical nonlinear Schr{ö}dinger equations on some metric graphs
Nabile Boussaïd, Jack Borthwick
We consider the existence of stationary wave solutions with prescribed mass to a supercritical nonlinear Schr{ö}dinger equation on a noncompact connected metric graph without a sma…
On spectral stability of one- and bi-frequency solitary waves in Soler model in (3+1)D
Nabile Boussaïd, Andrew Comech, Niranjana Kulkarni
For the nonlinear Dirac equation with scalar self-interaction (the Soler model) in three spatial dimensions, we consider the linearization at solitary wave solutions and find the i…
Virtual levels and virtual states of linear operators in Banach spaces. Applications to Schroedinger operators
Nabile Boussaid, Andrew Comech
We develop a general approach to virtual levels in Banach spaces. We show that virtual levels admit several characterizations which are essentially equivalent: (1) there are corres…
Some remarks on a minimization problem associated to a fourth order nonlinear Schrödinger equation
Nabile Boussaïd, Antonio J. Fernández, Louis Jeanjean
Let , , and . In the present paper, we study, for given, the constrained minimization problem \begin{equation*} \label{MinL2fixed} m(c):=…
Nonrelativistic asymptotics of solitary waves in the Dirac equation with the Soler-type nonlinearity
Nabile Boussaid, Andrew Comech
We use the perturbation theory to build solitary wave solutions to the nonlinear Dirac equation in , , with the Soler-type nonlinear term $f(…