Damped and Driven Breathers and Metastability

TL;DR

This paper proves the existence of a new family of periodic solutions called breathers in damped and driven discrete nonlinear Schrödinger equations, offering a better understanding of metastable states and their stability in lattice systems.

Contribution

It introduces a novel family of breathers in driven-damped lattice systems and analyzes their stability, providing more accurate descriptions of metastable behaviors.

Findings

Existence of a new family of breathers in the system.

Breathers exhibit near-tangent stability with small positive eigenvalues.

Solutions slide along the breather family surface for extended periods.

Abstract

In this article we prove the existence of a new family of periodic solutions for discrete, nonlinear Schrodinger equations subject to spatially localized driving and damping. They provide an alternate description of the metastable behavior in such lattice systems which agrees with previous predictions for the evolution of metastable states while providing more accurate approximations to these states. We analyze the stability of these breathers, finding a very small positive eigenvalue whose eigenvector lies almost tangent to the surface of the cylinder formed by the family of breathers. This causes solutions to slide along the cylinder without leaving its neighborhood for very long times.