Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2407.15088

Stationary Solitons in discrete NLS with non-nearest neighbour interactions

Vassilis M. Rothos·Stavros Anastassiou·Katerina G. Hadjifotinou
View original source ↗Read source document ↗Export metadata ↓

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.

Explore related subjects

math.DSmath-phmath.APmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Vassilis M. Rothos, Stavros Anastassiou, Katerina G. Hadjifotinou. 2024-07-21. Stationary Solitons in discrete NLS with non-nearest neighbour interactions. https://doi.org/10.1098/rspa.2024.0539

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Effective equidistribution of orbits under semisimple groups on congruence quotients

We prove an effective equidistribution result for periodic orbits of semisimple groups on congruence quotients of an ambient semisimple group.This extends a previous work of Einsiedler, Margulis and Venkatesh. The main new feature is that we allow for periodic orbits of semisimple groups with nontrivial centralizer in the ambient group. Our proof uses crucially an effective closing lemma from work of the author with Lindenstrauss, Margulis,Mohammadi, and Shah.

math.DS↗
arXiv2026

Generalized entropy of measure-induced maps

A classical result by E. Glasner and B. Weiss states that the topological entropy of a map $f$ is zero if and only if the topological entropy of its measure-induced map $f_*$ is zero, where $f_*$ is defined as the push-forward of a measure. In this work, we use generalized entropy to distinguish the complexity of these maps and prove that the measure-induced map is much more complex than the original map. Moreover, we introduce the generalized mean dimension, an invariant that is useful for distinguishing dynamical systems with zero mean dimension, including those with the small-boundary property, and we show a relationship between this new invariant and generalized entropy.

math.DS↗
arXiv2026

The endpoint problem for $\varepsilon$-hypercyclicity

For a fixed $0<\varepsilon<1$, F. Bayart asked in 2024 whether there exists an operator $T$ such that, for every $0<δ<1$, $T$ is $δ$-hypercyclic if and only if $δ\in[\varepsilon,1)$. We answer this question affirmatively by constructing a weighted backward shift on $\ell_2(\mathbb N_0,\ell_2(\mathbb N_0))$ with this property.

math.DS↗