Small and large data scattering for the dispersion-managed NLS

Abstract: We prove several scattering results for dispersion-managed nonlinear Schr\"odinger equations. In particular, we establish small-data scattering for both intercritical' andmass-subcritical' powers by suitable modifications of the standard approach via Strichartz estimates. In addition, we prove scattering for arbitrary data in a weighted Sobolev space for intercritical powers by establishing a pseudoconformal energy estimate. We also rule out (unmodified) scattering for sufficiently low powers. Finally, we give some remarks concerning blowup for the focusing equation.