2. Symmetries 2.1. Hamiltonian formulation 2.2. The symmetries 2.3. Group therapy 2.4.
Complete integrability 3. The local theory 3.1. Dispersive and Strichartz inequalities 3.2. The …

R.–On démontre des identités de type viriel bilinéaire pour l'équation de
Schrödinger nonlinéaire, qui peuvent être vues comme des extensions des inégalités …

We prove new interaction Morawetz-type (correlation) estimates in one and two dimensions.
In dimension 2 the estimate corresponds to the nonlinear diagonal analogue of Bourgain's …

We prove scattering for the defocusing fourth-order Schrödinger equation in low spatial
dimensions (1⩽ n⩽ 4). Inspired by the method in (Pausader 2010 Indiana Univ. Math. J. 59 …

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We prove global well-posedness and scattering in H 1 for the defocusing nonlinear
Schrödinger equations\left {(i\partial_t+\Delta_g) u= u| u|^ 2 σ;\u (0)= ϕ,. on the hyperbolic …

We consider the one-dimensional nonlinear Schr\" odinger equation with a nonlinearity of
degree $ p> 1$. We exhibit measures on the space of initial data for which we describe the …

We prove global well-posedness for low regularity data for the L 2-critical defocusing
nonlinear Schrödinger equation (NLS) in 2D. More precisely, we show that a global solution …

Recently several authors have developed multilinear and in particular quadratic extensions
of the classical Morawetz inequality. Those extensions provide (among other results) an …

We prove global well-posedness for low regularity data for the one dimensional quintic
defocusing nonlinear Schrödinger equation. Precisely we show that a unique and global …