Zobrazeno 1 - 10
of 208
pro vyhledávání: '"Dinh, van Duong"'
Autor:
Dinh, van Duong, Rougerie, Nicolas
We study the mean-field limit of the 1D bosonic canonical ensemble in a superharmonic trap. This is the regime with temperature proportional to particle number, both diverging to infinity, and correspondingly scaled interactions. We prove that the li
Externí odkaz:
http://arxiv.org/abs/2412.13597
In this paper, we investigate the Gibbs measures associated with the focusing nonlinear Schr\"odinger equation with an anharmonic potential. We establish a dichotomy for normalizability and non-normalizability of the Gibbs measures in one dimension a
Externí odkaz:
http://arxiv.org/abs/2312.06232
Autor:
Dinh, Van Duong, Rougerie, Nicolas
We consider the one dimensional cubic nonlinear Schr{\"o}dinger equation with trapping potential behaving like |x| s (s > 1) at infinity. We construct Gibbs measures associated to the equation and prove that the Cauchy problem is globally well-posed
Externí odkaz:
http://arxiv.org/abs/2301.02544
Autor:
Dinh, Van Duong, Keraani, Sahbi
We consider a class of biharmonic nonlinear Schr\"odinger equations with a focusing inhomogeneous power-type nonlinearity \[ i\partial_t u -\Delta^2 u+\mu\Delta u +|x|^{-b} |u|^\alpha u=0, \quad \left. u\right|_{t=0}=u_0 \in H^2(\mathbb{R}^d) \] with
Externí odkaz:
http://arxiv.org/abs/2211.11824
Autor:
Dinh, Van Duong, Esfahani, Amin
We study a system of inhomogeneous nonlinear Schr\"odinger equations that emerge in optical media with a $\chi^{(2)}$ nonlinearity. This nonlinearity, whose local strength is subject to a cusp-shaped spatial modulation, $\chi^{(2)}\sim |x|^{-\alpha}$
Externí odkaz:
http://arxiv.org/abs/2209.10947
Publikováno v:
SIAM J. MATH. ANAL. Vol. 56 (2024), No. 3, pp 3110-3143
We give a new proof of the scattering below the ground state energy level for a class of nonlinear Schr\"odinger equations (NLS) with mass-energy intercritical competing nonlinearities. Specifically, the NLS has a focusing leading order nonlinearity
Externí odkaz:
http://arxiv.org/abs/2209.01600
We study the ground states of a 2D focusing non-linear Schr\"odinger equation with rotation and harmonic trapping. When the strength of the interaction approaches a critical value from below, the system collapses to a profile obtained from the optimi
Externí odkaz:
http://arxiv.org/abs/2208.08317
Autor:
Dinh, Van Duong
We study the existence and stability of standing waves associated to the Cauchy problem for the nonlinear Schr\"odinger equation (NLS) with a critical rotational speed and an axially symmetric harmonic potential. This equation arises as an effective
Externí odkaz:
http://arxiv.org/abs/2201.02682
Autor:
Dinh, Van Duong
In this paper, we revisit the Cauchy problem for the three dimensional nonlinear Schr\"odinger equation with a constant magnetic field. We first establish sufficient conditions that ensure the existence of global in time and finite time blow-up solut
Externí odkaz:
http://arxiv.org/abs/2201.02690
We investigate the Cauchy problem for the focusing inhomogeneous nonlinear Schr\"odinger equation $i \partial_t u + \Delta u = - |x|^b |u|^{p-1} u$ in the radial Sobolev space $H^1_{\text{rad}}(\mathbb{R}^N)$, where $b>0$ and $p>1$. We show the globa
Externí odkaz:
http://arxiv.org/abs/2107.01479