CIMMS Lunchtime Series: Instabilities in the Forced Truncated NLS

Eli Shlizerman, Faculty of Mathematics and CS, Weizmann Institute of Science

We analyze the truncated forced non-linear Schrödinger (NLS)
model using a novel framework in which a hierarchy of bifurcations
is constructed. Consequently, we provide insights regarding its
global structure and the type of instabilities which appear in it.
In particular, we show that a parabolic resonance mechanism of
instability arises in the relevant parameter regime of this model.
The analogous behavior in the NLS pde is discussed.