Solitons in a modified discrete nonlinear Schroedinger equation

TL;DR

This paper investigates the properties and stability of solitons in a modified discrete nonlinear Schrödinger equation, revealing insights into their existence, stability, and dynamics, including management of the Peierls-Nabarro barrier and ballistic propagation.

Contribution

It provides a detailed analysis of bulk and surface modes in the mDNLS equation, including stability and evolution, highlighting the robustness of discrete soliton behavior compared to the standard DNLS.

Findings

Fundamental bulk mode has no power threshold.

Surface mode requires a minimum power to exist.

Long-term propagation becomes ballistic as nonlinear effects diminish.

Abstract

We study the bulk and surface nonlinear modes of the modified one-dimensional discrete nonlinear Schroedinger (mDNLS) equation. A linear and a modulational stability analysis of the lowest-order modes is carried out. While for the fundamental bulk mode there is no power threshold, the fundamental surface mode needs a minimum power level to exist. Examination of the time evolution of discrete solitons in the limit of strongly localized modes, suggests ways to manage the Peierls- Nabarro barrier, facilitating in this way a degree of steering. The long-time propagation of an initially localized excitation shows that, at long evolution times, nonlinear effects become negligible and as a result, the propagation becomes ballistic. The similarity of all these results to the ones obtained for the DNLS equation, points out to the robustness of the discrete soliton phenomenology.