Small and large data scattering for the dispersion-managed NLS

TL;DR

This paper proves various scattering results for dispersion-managed nonlinear Schrödinger equations, including small-data and weighted space scattering, and discusses blowup phenomena.

Contribution

It introduces new scattering results for intercritical and mass-subcritical powers, extending standard methods with modifications and energy estimates.

Findings

Small-data scattering for intercritical and mass-subcritical powers.

Scattering for arbitrary data in weighted Sobolev spaces.

Ruling out scattering for low powers.

Abstract

We prove several scattering results for dispersion-managed nonlinear Schr\"odinger equations. In particular, we establish small-data scattering for both `intercritical' and `mass-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.