Stationary Solitons in discrete NLS with non-nearest neighbour interactions

TL;DR

This paper constructs stationary discrete solitons in a one-dimensional extended Discrete NLS model with long-range, non-nearest neighbour interactions, revealing bistability and potential applications in controllable switching.

Contribution

It introduces a method to accurately construct stationary solitons in a long-range interaction Discrete NLS model, expanding understanding of their properties.

Findings

Stationary solitons can be accurately constructed in the extended model.

Long-range interactions induce bistability in soliton solutions.

The model has potential applications in biological energy transport and controllable switching.

Abstract

The aim of this paper is to provide a construction of stationary discrete solitons in an extended one-dimensional Discrete NLS model with non-nearest neighbour interactions. These models, models of the type with long-range interactions were studied in various other contexts. In particular, it was shown that, if the interaction strength decays sufficiently slowly as a function of distance, it gives rise to bistability of solitons, which may find applications in their controllable switching. Dynamical lattices with long-range interactions also serve as models for energy and charge transport in biological molecules. Using a dynamical systems method we are able to construct, with great accuracy, stationary discrete solitons for our model, for a large region of the parameter space.