We consider the following Hamiltonian equation on a special manifold of rational functions:
where denotes the Szegő projector on the Hardy space of the circle . The equation with was first introduced by Gérard and Grellier as a toy model for totally nondispersive evolution equations. We establish the following properties for this equation. For , any compact subset of initial data leads to a relatively compact subset of trajectories. For , there exist trajectories on which high Sobolev norms exponentially grow in time.
"Large-time blowup for a perturbation of the cubic Szegő equation." Anal. PDE 7 (3) 717 - 731, 2014. https://doi.org/10.2140/apde.2014.7.717