In any dimension N≥ 1, for given mass m> 0 and for the C 1 energy functional I (u):= 1 2∫
RN|∇ u| 2 dx-∫ RNF (u) dx, we revisit the classical problem of finding conditions on F∈ C 1 …

For the Schrödinger equation with a cubic-quintic, focusing-defocusing nonlinearity in one
space dimension, we prove the asymptotic stability of solitary waves for a large range of …

In any dimension N≥ 1, for given mass m> 0 and when the C 1 energy functional I (u):= 1
2∫ ℝ N|∇ u| 2 dx−∫ ℝ NF (u) dx is coercive on the mass constraint S m:= u∈ H 1 (ℝ N)|∥ …

Optical fibers, long an enabling technology for telecommunications, are proving to play a
central role in a growing number of modern applications, starting from high speed broad …

We consider the large data scattering problem for the 2D and 3D cubic-quintic nonlinear
Schrödinger equation in the focusing-focusing regime. Our attention is firstly restricted to the …

We consider the cubic-quintic nonlinear Schrödinger equation in two space dimensions. For
this model, X. Cheng established scattering for H 1 data with mass strictly below that of the …

We consider the nonlinear Schr\" odinger equation with combined nonlinearities, where the
leading term is an intracritical focusing power-type nonlinearity, and the perturbation is given …

We consider a Schrödinger equation with a nonlinearity which is a general perturbation of a
power nonlinearity. We construct a profile decomposition adapted to this nonlinearity. We …

In this article, we prove the global well-posedness and scattering of the cubic focusing
infinite coupled nonlinear Schr\" odinger system on $\mathbb {R}^ 2$ below the threshold in …

We demonstrate transmission stabilization against radiation emission by frequency-
dependent linear gain-loss and perturbation-induced frequency shifting for solitons of the …