Construction of the discrete breathers and a simple physical interpretation of their existence

TL;DR

This paper introduces a straightforward numerical method based on pair synchronization to construct discrete breathers in nonlinear Hamiltonian lattices, providing a simple physical interpretation of their existence as localized, time-periodic solutions.

Contribution

The paper presents a new, simple numerical approach for constructing discrete breathers and offers a physical interpretation of their existence in nonlinear lattices.

Findings

Method successfully constructs exact breather solutions

Provides a physical interpretation of breathers as localized, periodic objects

Applicable to various nonlinear Hamiltonian lattices

Abstract

We present a simple numerical method for the discrete breather construction based on the idea of the pair synchronization of the particles involved in the breather vibration. It can be used for obtaining exact breather solutions in nonlinear Hamiltonian lattices of different types. We illustrate the above method using chains of the coupled Duffng oscillators. With some additional approximation, the pair synchronization method leads to a very simple physical interpretation of the existence of the exact breathers as strictly time-periodic and spatially localized dynamical objects.