We consider the cubic-quintic nonlinear Schrödinger equation of up to three space
dimensions. The cubic nonlinearity is thereby focusing while the quintic one is defocusing …

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 …

We revisit the scattering result of Holmer and Roudenko (2008) on the radial focusing cubic
NLS in three space dimensions. Using the radial Sobolev embedding and a virial/Morawetz …

We consider the focusing energy-critical nonlinear Schr\" odinger equation $ iu_t+\Delta u=-|
u|^{4\over {d-2}} u $ in dimensions $ d\geq 5$. We prove that if a maximal-lifespan solution …

We consider the supercritical inhomogeneous nonlinear Schr\" odinger equation (INLS) $$
i\partial_t u+\Delta u+| x|^{-b}| u|^{2\sigma} u= 0, $$ where $(2-b)/N<\sigma<(2-b)/(N-2) …

The notion of an invariant manifold arises naturally in the asymptotic stability analysis of
stationary or standing wave solutions of unstable dispersive Hamiltonian evolution …

We show scattering versus blow-up dichotomy below the ground state energy for the
focusing nonlinear Klein–Gordon equation, in the spirit of Kenig and Merle for the H 1 critical …

The purpose of this paper is to study well-posedness of the initial value problem (IVP) for the
inhomogeneous nonlinear Schrödinger equation (INLS) iu t+ Δ u+ λ| x|− b| u| α u= 0, where …

We consider the focusing cubic nonlinear Schrödinger equation with inverse-square
potential in three space dimensions. We identify a sharp threshold between scattering and …

For the 3D focusing cubic nonlinear Schrödinger equation, scattering of H 1 solutions inside
the (scale invariant) potential well was established by Holmer and Roudenko (radial case) …