Section: New Results

New results on waveguides with mixed diffusion

In [21], [8], [22], D. Bonheure, J.-B. Casteras and collaborators obtained new results on the existence and qualitative properties of waveguides for a mixed-diffusion NLS equation. In particular, they proved the first existence results for waveguides with fixed mass and provided several qualitative descriptions of these. They also showed that the ground-state solutions are instable by finite (or infinite) time blow-up improving a recent result of Boulenger and Lenzmann and answering a conjecture of Baruch and Fibich.