2024/07/21 by Rothos, Vassilis M., Anastassiou, Stavros, Hadjifotinou, Katerina G. · 1 citation
#Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2407.15088
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.