Staggered and short period solutions of the Saturable Discrete Nonlinear Schr\"odinger Equation

TL;DR

This paper explores the existence and stability of staggered, short period, and pulse-like solutions in the saturable discrete nonlinear Schrödinger equation, revealing their stability properties and the zero Peierls-Nabarro barrier for solitons.

Contribution

It demonstrates the presence of various stable solutions in the saturable DNLS model, including staggered and short period solutions, and analyzes their stability and energy barriers.

Findings

Staggered and short period solutions are mostly stable.

Pulse-like solitons have a zero Peierls-Nabarro barrier.

The model admits multiple stable localized solutions.

Abstract

We point out that the nonlinear Schr{\"o}dinger lattice with a saturable nonlinearity also admits staggered periodic as well as localized pulse-like solutions. Further, the same model also admits solutions with a short period. We examine the stability of these solutions and find that the staggered as well as the short period solutions are stable in most cases. We also show that the effective Peierls-Nabarro barrier for the pulse-like soliton solutions is zero.