Moving discrete breathers?

TL;DR

This paper defines moving localized objects in discrete nonlinear lattices, derives relations between their properties, proposes algorithms to find them, and discusses extensions to higher dimensions.

Contribution

It introduces analytical relations and numerical methods for moving discrete breathers and kinks, advancing understanding of their dynamics in nonlinear lattices.

Findings

Derived relations between frequency, velocity, and localization length.

Developed numerical algorithms for finding moving localized solutions.

Discussed potential generalizations to higher-dimensional lattices.

Abstract

We give definitions for different types of moving spatially localized objects in discrete nonlinear lattices. We derive general analytical relations connecting frequency, velocity and localization length of moving discrete breathers and kinks in nonlinear one-dimensional lattices. Then we propose numerical algorithms to find these solutions. Finally we discuss generalizations to higher dimensional lattices.