5 papers · 1 filter
Finite-time blow-up for the four-dimensional mass-critical quadratic nonlinear Schrödinger system without mass resonance
Ngoc Uyen Cong Nguyen, Van Duong Dinh
We study the focusing quadratic nonlinear Schrödinger system \[ \begin{cases} i\partial_t u+Δu=-2v\overline{u}, \\ i\partial_t v+κΔv=-u^2, \end{cases} \qquad (t,x)\in I\times\mathb…
From bosonic canonical ensembles to non-linear Gibbs measures
van Duong Dinh, Nicolas Rougerie
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 i…
Statistical mechanics of the radial focusing nonlinear Schrödinger equation in general traps
Van Duong Dinh, Nicolas Rougerie, Leonardo Tolomeo +1
In this paper, we investigate the Gibbs measures associated with the focusing nonlinear Schrödinger equation with an anharmonic potential. We establish a dichotomy for normalizabi…
Scattering for non-radial 3D NLS with combined nonlinearities: the interaction Morawetz approach
Jacopo Bellazzini, Van Duong Dinh, Luigi Forcella
We give a new proof of the scattering below the ground state energy level for a class of nonlinear Schrödinger equations (NLS) with mass-energy intercritical competing nonlinearit…
A system of inhomogeneous NLS arising in optical media with a nonlinearity, part I : Dynamics
Van Duong Dinh, Amin Esfahani
We study a system of inhomogeneous nonlinear Schrödinger equations that emerge in optical media with a nonlinearity. This nonlinearity, whose local strength is subject…