The stability of nonlinear waves has a distinguished history and an abundance of richly
structured yet accessible examples, which makes it not only an important subject but also an …

In this book we consider solution branches and bifurcations in nonlinear partial differential
equations (PDEs) as models from science (and some economics). Given a nonlinear PDE …

We consider the focusing (attractive) nonlinear Schrödinger (NLS) equation with an external,
symmetric potential which vanishes at infinity and supports a linear bound state. We prove …

We consider standing waves in the focusing nonlinear Schrödinger (NLS) equation on a
dumbbell graph (two rings attached to a central line segment subject to the Kirchhoff …

In this work we analyze PT-symmetric double-well potentials based on a two-mode picture.
We reduce the problem into a PT-symmetric dimer and illustrate that the latter has effectively …

Nonlinear dispersive waves are wave phenomena resulting from the interacting effects of
nonlinearity and dispersion. Dispersion refers to the property that waves of different …

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 …

In this paper, we give an alternative proof for the asymptotic stability of solitons for nonlinear
Schrödinger equations with internal modes. The novel idea is to use “refined profiles” …

We pose the problem of transferring a Bose–Einstein Condensate (BEC) from one side of a
double-well potential to the other as an optimal control problem for determining the time …

We describe the asymptotic behavior of small energy solutions of an NLS with a trapping
potential, generalizing work of Soffer and Weinstein, and of Tsai and Yau. The novelty is that …