We prove an analogue of a classical asymptotic stability result of standing waves of the Schrödinger equation originating in work by Soffer and Weinstein. Specifically, our result is a transposition… (More)

We consider radial solutions of a mass supercritical monic NLS and we prove the existence of a set, which looks like a hypersurface, in the space of finite energy functions, invariant for the flow… (More)

We consider examples of discrete nonlinear Schrödinger equations in Z admitting ground states which are orbitally but not asymptotically stable in l(Z). The ground states contain internal modes which… (More)

We consider a nonlinear Schrödinger equation iut − h0u+ β(|u|)u = 0 , (t, x) ∈ R× R, with h0 = − d 2 dx2 + P (x) a Schrödinger operator with finitely many spectral bands. We assume the existence of… (More)

This is a revision of the author’s paper ”On asymptotic stability in energy space of ground states of NLS in 1D” [C3]. We correct an error in Lemma 5.4 [C3] and we simplify the smoothing argument. §

We prove the instability of a “critical” solitary wave of the generalized Korteweg – de Vries equation, the one with the speed at the border between the stability and instability regions. The… (More)

We extend a result on dispersion for solutions of the linear Schrödinger equation, proved by Firsova for operators with finitely many energy bands only, to the case of smooth potentials in 1D with… (More)

We add to a kink, which is a 1 dimensional structure, two transversal directions. We then check its asymptotic stability with respect to compactly supported perturbations in 3D and a time evolution… (More)

We consider the stability problem for standing waves of nonlinear Dirac models. Under a suitable definition of linear stability, and under some restriction on the spectrum, we prove at the same time… (More)