Super-exponential decay of Diffraction Managed Solitons

TL;DR

This paper proves that solutions to the diffraction managed discrete nonlinear Schrödinger equation decay super-exponentially when the average diffraction vanishes, and also confirms the existence of diffraction managed solitons in this regime.

Contribution

It provides rigorous decay estimates for breather solutions and a simple proof of soliton existence in the diffraction management context.

Findings

Solutions decay super-exponentially at vanishing average diffraction

Existence of diffraction managed solitons is established

Method offers a straightforward proof approach

Abstract

This is the second part of a series of papers where we develop rigorous decay estimates for breather solutions of an averaged version of the non-linear Schr\"odinger equation. In this part we study the diffraction managed discrete non-linear Schr\"odinger equation, an equation which describes coupled waveguide arrays with periodic diffraction management geometries. We show that, for vanishing average diffraction, all solutions of the non-linear and non-local diffraction management equation decay super-exponentially. As a byproduct of our method, we also have a simple proof of existence of diffraction managed solitons in the case of vanishing average diffraction.