Discrete breathers

S Flach, CR Willis - Physics reports, 1998 - Elsevier
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete
breathers. These solutions are time-periodic and (typically exponentially) localized in space …

Discrete breathers—advances in theory and applications

S Flach, AV Gorbach - Physics Reports, 2008 - Elsevier
Nonlinear classical Hamiltonian lattices exhibit generic solutions—discrete breathers. They
are time-periodic and (typically exponentially) localized in space. The lattices have discrete …

[BOOK][B] Optical solitons: from fibers to photonic crystals

YS Kivshar, GP Agrawal - 2003 - books.google.com
The current research into solitons and their use in fiber optic communications is very
important to the future of communications. Since the advent of computer networking and …

The discrete nonlinear Schrödinger equation: a survey of recent results

PG Kevrekidis, KØ Rasmussen… - International Journal of …, 2001 - World Scientific
In this paper we review a number of recent developments in the study of the Discrete
Nonlinear Schrödinger (DNLS) equation. Results concerning ground and excited states …

Dynamics of discrete solitons in the fractional discrete nonlinear Schrödinger equation with the quasi-Riesz derivative

M Zhong, BA Malomed, Z Yan - Physical Review E, 2024 - APS
We elaborate a fractional discrete nonlinear Schrödinger (FDNLS) equation based on an
appropriately modified definition of the Riesz fractional derivative, which is characterized by …

Fractional dynamics of systems with long-range interaction

VE Tarasov, GM Zaslavsky - Communications in Nonlinear Science and …, 2006 - Elsevier
We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-
range powerwise interaction defined by a term proportional to 1/∣ n− m∣ α+ 1. Continuous …

Fractional dynamics of coupled oscillators with long-range interaction

VE Tarasov, GM Zaslavsky - Chaos: An Interdisciplinary Journal of …, 2006 - pubs.aip.org
We consider a one-dimensional chain of coupled linear and nonlinear oscillators with long-
range powerwise interaction. The corresponding term in dynamical equations is proportional …

Continuous limit of discrete systems with long-range interaction

VE Tarasov - Journal of Physics A: Mathematical and General, 2006 - iopscience.iop.org
Discrete systems with long-range interactions are considered. Continuous medium models
as continuous limit of discrete chain system are defined. Long-range interactions of chain …

[HTML][HTML] Point-wise error estimate of a conservative difference scheme for the fractional Schrödinger equation

P Wang, C Huang, L Zhao - Journal of Computational and Applied …, 2016 - Elsevier
In this paper, a new conservative difference scheme is proposed for solving the nonlinear
space-fractional Schrödinger equation. The Riesz space-fractional derivative is …

Models for energy and charge transport and storage in biomolecules

SF Mingaleev, PL Christiansen, YB Gaididei… - Journal of biological …, 1999 - Springer
Two models for energy and charge transport and storage in biomolecules are considered. A
model based on the discrete nonlinear Schrödinger equation with long-range dispersive …