Breathers as Metastable States for the Discrete NLS equation

TL;DR

This paper investigates metastable states in weakly damped Hamiltonian systems, focusing on breather solutions in the discrete nonlinear Schrödinger (NLS) equation, and provides analytical and numerical insights into energy transport inhibition.

Contribution

It introduces a perturbative approach to compute breather solutions in the discrete NLS equation and derives estimates for system drift along these metastable states.

Findings

Breather solutions can be computed perturbatively to arbitrary order.

The derived drift estimates are numerically verified and shown to be optimal.

Metastable states significantly inhibit energy transport in the model.

Abstract

We study metastable motions in weakly damped Hamiltonian systems. These are believed to inhibit the transport of energy through Hamiltonian, or nearly Hamiltonian, systems with many degrees of freedom. We investigate this question in a very simple model in which the breather solutions that are thought to be responsible for the metastable states can be computed perturbatively to an arbitrary order. Then, using a modulation hypothesis, we derive estimates for the rate at which the system drifts along this manifold of periodic orbits and verify the optimality of our estimates numerically.