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 …

In this paper we first prove a general result about the uniqueness and non-degeneracy of
positive radial solutions to equations of the form Δ u+ g (u)= 0 Δ u+ g (u)= 0. Our result …

We introduce and implement a method to compute stationary states of nonlinear
Schrödinger equations on metric graphs. Stationary states are obtained as local minimizers …

arXiv:2009.00573v1 [math.AP] 1 Sep 2020 Page 1 arXiv:2009.00573v1 [math.AP] 1 Sep 2020
A survey on asymptotic stability of ground states of nonlinear Schrödinger equations II Scipio …

The Akhmediev breather (AB) and its M-breather generalisation, hereafter called AB M, are
exact solutions of the focusing NLS equation periodic in space and exponentially localised …

We study the dynamics of waves, oscillations, and other spatio-temporal patterns in
stochastic evolution systems, including SPDE and stochastic integral equations …

The stability of periodic traveling wave solutions to dispersive PDEs with respect to'arbitrary'
perturbations is still widely open. The focus is put here on stability with respect to …

In this paper we give a new and simplified proof of the theorem on selection of standing
waves for small energy solutions of the nonlinear Schrödinger equations (NLS) that we gave …

We study the point spectrum of the linearization at a solitary wave solution ϕ ω (x) e− i ω t to
the nonlinear Dirac equation in R n, for all n≥ 1, with the nonlinear term given by f (ψ⁎ β ψ) …

We establish the nonlinear stability of N-soliton solutions of the modified Korteweg–de Vries
(mKdV) equation. The N-soliton solutions are global solutions of mKdV behaving at (positive …