We provide a simple sufficient condition in an abstract framework to deduce the existence
and completeness of wave operators (resp., modified wave operators) on Sobolev spaces …

We are concerned with the global behavior of the solutions of the focusing mass
supercritical nonlinear Schr {\" o} dinger equation under partial harmonic confinement. We …

In this paper, we study a class of nonlinear Schrödinger equations (NLS) with potential i ∂
_t u+ Δ u-Vu= ±| u|^ α u,\quad (t, x) ∈\mathbb R *\mathbb R^ 3, i∂ tu+ Δ uV u=±| u| α u,(t …

We consider a class of 1D NLS perturbed with a steplike potential. We prove that the
nonlinear solutions satisfy the double scattering channels in the energy space. The proof is …

We prove $ H^{1} $ scattering for a defocusing NLS on the line with fully variable
coefficients. The result is proved by adapting the Kenig--Merle scheme to a non translation …

We study the large time behavior of global energy class solutions of the one dimensional
nonlinear Schr\" odinger equation with a general localized potential term and a defocusing …

In this paper, we investigate the global well-posedness and $ H^{1} $ scattering theory for a
3d energy-critical Schr\" odinger equation under the influence of magnetic dipole interaction …

PM_78-1_04_Tzvetkov 101..128 Page 1 Portugal. Math. (NS) 6 2021 Sociedade Portuguesa de
Matemįtica Vol. 78, Fasc. 1, 2021, 101–128 Published by EMS Press DOI 10.4171/PM/2062 On …

We study the scattering theory for the Schrödinger and wave equations with rough potentials
in a scale of homogeneous Sobolev spaces. The first half of this paper is concerned with an …

We study global dynamics of the solution to the Cauchy problem for the focusing semilinear
Schrödinger equation with a linear potential on the real line R:(NLS V){i∂ t u+∂ x 2 u− V u+ …