Zobrazeno 1 - 10
of 63
pro vyhledávání: '"Boussaïd, Nabile"'
We present sufficient conditions for the exact controllability in projection of the linear Schr{\"o}dinger equations in the case where the spectrum of the free Hamiltonian is pure point. We consider the general case in which the Hamiltonian may be no
Externí odkaz:
http://arxiv.org/abs/2404.08290
In this paper, we study a new type of inverse problem on warped product Riemannian manifolds with connected boundary that we name warped balls. Using the symmetry of the geometry, we first define the set of Regge poles as the poles of the meromorphic
Externí odkaz:
http://arxiv.org/abs/2203.13850
Autor:
Boussaid, Nabile, Comech, Andrew
We review the concept of the limiting absorption principle and its connection to virtual levels of operators in Banach spaces.
Comment: 25 pages. arXiv admin note: text overlap with arXiv:2101.11979
Comment: 25 pages. arXiv admin note: text overlap with arXiv:2101.11979
Externí odkaz:
http://arxiv.org/abs/2109.07108
Autor:
Boussaid, Nabile, Comech, Andrew
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 corresponding virtual states (from a certain larger space); (2) there is no
Externí odkaz:
http://arxiv.org/abs/2101.11979
Autor:
Boussaid, Nabile, Cacciapuoti, Claudio, Carlone, Raffaele, Comech, Andrew, Noja, Diego, Posilicano, Andrea
We consider the nonlinear Dirac equation with Soler-type nonlinearity concentrated at one point and present a detailed study of the spectrum of linearization at solitary waves. We then consider two different perturbations of the nonlinearity which br
Externí odkaz:
http://arxiv.org/abs/2006.03345
Some remarks on a minimization problem associated to a fourth order nonlinear Schr\'odinger equation
Let $\gamma > 0\,$, $\beta > 0\,$, $\alpha > 0$ and $0 < \sigma N < 4$. In the present paper, we study, for $c > 0$ given, the constrained minimization problem \begin{equation*} \label{MinL2fixed} m(c):=\inf_{u\in S (c) }E(u), \end{equation*} where \
Externí odkaz:
http://arxiv.org/abs/1910.13177
In this paper we present an extension to the case of $L^1$-controls of a famous result by Ball--Marsden--Slemrod on the obstruction to the controllability of bilinear control systems in infinite dimensional spaces.
Externí odkaz:
http://arxiv.org/abs/1903.05846
Autor:
Boussaid, Nabile, Comech, Andrew
We construct bi-frequency solitary waves of the nonlinear Dirac equation with the scalar self-interaction (the Soler model) and the Dirac--Klein--Gordon with Yukawa self-interaction. These solitary waves provide a natural implementation of qubit and
Externí odkaz:
http://arxiv.org/abs/1711.05654
Autor:
Boussaid, Nabile, Comech, Andrew
We study the point spectrum of the linearization at a solitary wave solution $\phi_\omega(x)e^{-\mathrm{i}\omega t}$ to the nonlinear Dirac equation in $\mathbb{R}^n$, $n\ge 1$, with the nonlinear term given by $f(\psi^*\beta\psi)\beta\psi$ (known as
Externí odkaz:
http://arxiv.org/abs/1705.05481
Nonrelativistic asymptotics of solitary waves in the Dirac equation with the Soler-type nonlinearity
Autor:
Boussaid, Nabile, Comech, Andrew
Publikováno v:
SIAM J. Math. Anal. 49 (2017), 2527--2572
We use the perturbation theory to build solitary wave solutions $\phi_\omega(x)e^{-i\omega t}$ to the nonlinear Dirac equation in $\mathbb{R}^n$, $n\ge 1$, with the Soler-type nonlinear term $f(\bar\psi\psi)\beta\psi$, with $f(\tau)=|\tau|^k+o(|\tau|
Externí odkaz:
http://arxiv.org/abs/1606.07308