Decay estimates and smoothness for solutions of the dispersion managed non-linear Schr\"odinger equation

TL;DR

This paper investigates the decay and smoothness properties of solutions to the dispersion managed nonlinear Schrödinger equation with zero residual dispersion, demonstrating that solutions are both smooth and rapidly decaying using novel bilinear Strichartz estimates.

Contribution

Introduces new x-space bilinear Strichartz estimates to prove smoothness and rapid decay of solutions in the zero residual dispersion case.

Findings

Solutions are smooth and rapidly decaying.

New x-space bilinear Strichartz estimates are developed.

Decay and smoothness are established for the specific case studied.

Abstract

We study the decay and smoothness of solutions of the dispersion managed non-linear Schr\"odinger equation in the case of zero residual dispersion. Using new x-space versions of bilinear Strichartz estimates, we show that the solutions are not only smooth, but also fast decaying.