Damped and Driven Breathers and Metastability
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.
Cite
@article{arxiv.2101.10999,
title = {Damped and Driven Breathers and Metastability},
author = {Daniel A. Caballero and C. Eugene Wayne},
journal= {arXiv preprint arXiv:2101.10999},
year = {2022}
}
Comments
21 pages, 4 figures, This revision computes the stability of the damped and driven breathers perturbatively (previously this had been done partially numerically) and adds some additional numerical illustrations of the results